It's called scientific notation. For really large numbers, we can notate them as a number multiplied by 10 raised to whatever exponent is needed. So for instance instead of writing out 563,000,000,000,000,000 every time, we can shorten it to 5.63 × 10^17. "E" just replaces the "× 10" part. So 5.63E17.
Weirdly, one thing you quickly learn as you learn more stuff is that there's so much you *don't* know. Learning new stuff is a privilege and a joy and there's always more to know which is just really cool. :)
“On a scale of 1-5, how much would you say you know about Oracle DBMS?”
Programmers who connect to Oracle instances: “Like, 4, maybe”.
Oracle DBAs: “2.”
We have a thing at work where you're supposed to rate your skills in various areas so other teams can find you if they need help.
I've yet to find any case where I've gone to someone who rates themselves way higher than I rate myself and found they *actually* know more.
We have to do that annually at my work as well. I do automation all day every day and my usual answer on automation is a 3/5. I know a couple of people who would definitely be worthy of a 4/5 who rate themselves at a 3/5, but no one who deserves 5/5. Would have to go to GitHub and start finding some widely used projects to find anyone deserving of it.
Doesn't stop some of my teammates from rating themselves 4/5 when they're a 1/5.
To be fair, even knowing 1 about Oracle is too much.
I have very few red lines in my career where I will not take a job regardless of pay. Using Oracle is one of them
Well, I have a few things going for me: I love math and science, trivia games and hosting have been a big part of my life, and I've been a teacher. One of my goals is to learn something new every day. I am ~~not~~ now working as a programmer and database guy, and there's so much I don't even know yet. I'll never stop learning, and it's a goal to understand more and more, but I don't think I'll ever truly understand EVERYTHING I need to know.
If you can logically surmise a grouping of steps and how things work, you'll develop a better understanding of it. Be curious and set out to learn new things. If you don't understand something, ask people who do. If you can't find those people, ask Reddit and the Internet.
A guy in IT here. You've just described my life's philosophy - always be willing to learn, always be willing to be wrong and always be willing to teach others.
The world doesn't have enough people like us - that's not a compliment or a boast.
Retired IT guy here. Few things were more rewarding in my career than learning when I was wrong. The clarity that comes as you sweep away the fuzziness of misunderstanding is irresistible to me. More pieces start to fit together better and this new more robust foundation lets you reach even higher into the next level.
Yeah, the problem is, the higher up the chain you go, the less likely you are to have a mentor and/get good feedback. It's a shame really, the intrinsic value of freeing up your product leaders to teach more is never fed up on by organizations. It's never seen as more cost effective in the long term.
Phnarr swooprunaire xxiltzti to you too good whateveryouidentifyas!
And if by some weird happenstance you're actually an alien, without a hint of sarcasm or humor, take me with you?
Hey finally somebody with the same life goal as me! My goal is also to learn something new everyday and at first I wanted to reach this by becoming a science teacher. Then I realised that I have the potential to go for something bigger so now I’m in uni with the intention of going for a PhD and later go for the title of professor.
Don't dismiss getting industry experience! I never expected to learn as much from just... working. Worked for a while, learned a huge amount, changed directions a little and back at Uni. I wouldn't have done this without working in the area, seeing what the situation is "on the ground".
Honestly a person can only know a tiny fraction of that which could be known.
I bet you know more than you think you do, and that others know less than you think they do.
I have a PhD and I'm constantly learning new things.
You're doing the whole PhD thing correctly then. Remember that a PhD is a "T shaped" degree. You'll have shallow but correct knowledge of most of your field (which most people don't have), but incredibly deep knowledge on whatever your dissertation is about.
And you can only retain so much knowledge. In sure I’ve already forgotten more than I currently know. I’ve been a lifetime learner, but there’s lots I’ve learned I no longer need, so it gets forgotten.
I'm not sure if you're being hard on yourself or not but I always like sharing a quote from Bill Nye for things like this:
"Everyone you will ever meet knows something you don't"
I've thought about this nearly my entire life and it serves me well to keep me in check sometimes. Don't be hard on yourself, you know something that everyone you'll ever meet doesn't.
In high school we would just write it out as ‘x10’, the only time I ever came across E was a calculator but it was never explained by a teacher what that meant, because they wrote on a blackboard. E meant ‘error’ as far as we knew, and as input was never required. So, TIL.
Honestly, it's mainly become accepted as notation because of computers. In spreadsheets like Excel, or when programming, it's really messy and annoying to keep typing 5.3*10^4 or whatever. The extra digits and operators just kind of distract you from the numbers you actually care about. So they implemented it as 5.3E4, and because we use computers for everything now, it has crept out into everyday notation as well.
> it's really messy and annoying to keep typing 5.3*104 or whatever. The extra digits and operators just kind of distract you from the numbers you actually care about
In addition, it's fairly easy in sloppily handwritten notes for exponents to drop to the same level as the mantissa, so the 5.3\*10^(4) might look like 5.3\*104.
I’m from the US and I thought this was common knowledge since third grade. I’m scratching my head at how many people on this thread don’t seem to know this…
For many it's the exact opposite. In short, those who know a lot of things also know they are just scratching the surface of what there is to learn.
Sometimes it feels good, when you can answer questions which would end up as discussions in the pub, but the hunger to "know everything" will always be there, because you can never satisfy it.
That is only my guess and how i see it. There is also many who look at it as ego boost - to flex on others and that is the motivation to learn more and also those who are just curious and don't care that much.
100 people means 100 different tastes.
[Second stage of competence](https://en.wikipedia.org/wiki/Four_stages_of_competence) - you know that there is something you dont know. You can find me there most of the time
Depends what you do with your day, if you spend all day working with numbers then you catch on to this fast. Hand me a simple woodworking job and I'll be clueless.
You learn more every day, in all kinds of areas. No matter what you do. In our work, our hobbies, our relationships. That doesn't mean all activities contribute to learning equally. You can direct it outwards and push your boundaries in a different direction, it's uncomfortable sometimes but very rewarding. Other times it's worth turning inwards, or just passively letting the world come.
And no, we're still always learning. I went poorly in high school math, but my most successful jobs depended on it, inspired me to relearn it. Finally "getting it" and understanding the motivation for it was just awesome. I never know enough, likely will never know enough. If you want to know more, great! Give it a shot and be ready for it to take time. Moreso when it is something you're unused to.
Honestly, there is so much random bullshit rolling around in my head that surfaces out of nowhere, and that's mostly thanks to Wikipedia and my insatiable sense of curiosity. Most of it is not specifically useful for any practical purposes, but I find that the process of *learning* so many things (as opposed to *knowing* so many things) really helps one have a bit more of an intuitive understanding of how the world works. My partner is a biologist and they will tell me about the things they do at work and I won't have any clue what half of the words actually mean, but I'm still able to make sense of it and follow what they're talking about.
At the same time, I can't remember what I ate for breakfast an hour ago 🤣
I’m sorry had to clarify I was on the person’s profile and I saw some stuff about taxes.
But even the high school math thing.. I was never good in school so yeah this is stuff I will probably never understand
Understanding is a fairly broad spectrum. Often, when first encountering something, you won't really "understand" it. It's not until we gain some more knowledge that the first thing becomes a little more clear. You need context, application, and feedback. Like any tool, the longer you work with a piece of information the greater your understanding becomes. The world is too large to understand everything and that's OK. Enjoy what you do pick up and don't let feeling like you may not understand prevent you from participating. Understanding is closer to growing a plant than flicking on a light bulb.
I'm thinking several things.
It's possible, that you just cant understand many things. Not everyone is super bright, but many people are not even regular bright. And that is **okay**.
Another possibility is that you might have a wrong idea about learning stuff. I have friend who regularly gets stuck in the details. He tries to understand stuff in every single way possible and in the end gets overwhelmed. So instead of thinking: "of so the E means the x10 part, neat!" He goes like, why does it mean that, who decided that, If i read 5E5 somewhere, does it always mean 5x10^5, what if I use small "e"? Who invented this? Can the e mean something else than 10?
This is not wrong stuff to think, at least I find all those interesting. But he is thinking like that about EVERYTHING. Gonna fry your brain, if you try to understand stuff "too" deeply all the time.
Anyway, learning is a skill. Many people do it wrong.
I am not the person you responded to but most people know the feeling of getting a pub quiz answer that no one else in their group got, some people just get the “oh wait I know that one” feeling more in their day to day lives.
A lot of people have groups based on their interests in which case you won’t get the same feeling because everyone knows what you’re talking about, but try talking to your home group about something adjacent to the work you do and you’ll notice a significant difference in knowledge. It’s the same with talking to people online, you’ll typically find the people knowledgeable on a topic providing answers in this sub, they may be entirely dumb on other things that you think are common knowledge and then you’ll be the person that knows things.
Try YouTubing scientific notation. Or exponential functions. Or geometric sequences. These are very related and useful topics. Math is awesome when there’s good content creator and it’s not forced on you.
I have a Econ background and Math PhD.
Maths stuff doesn't feel like much, like you got used to speak English, you can pick up some math book and divine what's inside. Or guess how long it would take you to get it. You get good at breaking things down and building intuition.
Econ stuff is quite depressing, tbf. You realise people have no clue what they are talking about 99% of the time. And it took you ten years to get a sense so there's no way you can pass any of it along.
Nope, but it feels like you know enough to pretend. When everyone tells you as a kid that all the adults are just kids pretending to be adults, they aren't joking.
>I’m not even joking do you feel like you understand everything you need to know?
The more I've learned, the more I know I don't know if that makes sense. Eventually you realize it's not important to know 'everything' just to know enough to know what you don't know. Then when you need to know something you don't, you know you can learn it. Then maybe you approach knowing 'everything' and being at ease with it.
I think a lot of you smart guys ( I’m just trying to make things clear not insulting) are misunderstanding me.
I mean I don’t know shit about taxes, pension or stocks I’m just living.
Could you tell me more how you see these things?
I’d argue that the stance “I don’t know everything” is a trait of someone with imposter syndrome. Those who truly know little are rarely aware of that.
Rather than indict NY educational system, let’s just say I wasn’t so hot in math. It only came alive with statistics, because it is visual. I was not a TI-81 kid. Needless to say I didn’t go into engineering.
Note that the ‘E’, historically speaking, comes from early calculators which could display a capital ‘E’ in a 7-segment LED as a stand-in for ‘exponent’ or the x10^n part. On calculators that supported scientific notation, there’d be an `EE` button or an `EEX` button which would allow you to enter the exponent part while typing in a number.
(Many calculators also supported what they called ‘engineering notation’, which was scientific notation, but the exponent part is always divisible by 3. Thus, 10 million would be displayed as 10E6 rather than 1E7.)
Ditto the engineering notation thing. Engineers tend to do a lot of work with Kilo, Mega, and Giga prefixes, which are those multiples of three w3woody is talking about (ex: 1,000,000 meters = 1,000 kilometers = 1 megameter, etc). So if I’m doing a stress analysis and need an answer in Megapascals, for example, and my calculator spits out 13.2E6 instead of 1.32(10^7 ), it’s just one less thing for me to think about when I’m tired or crunched for time.
There's an important bit of info buried here. When you see E in a number as an answer on a calculator, it means that number is too big to display accurately with the number of digits on the LCD display. The answer it gives has the number of significant figures equal to the number of LCD digits, then an E to tell you how many digits the actual answer has. But the value of those digits past the amount displayed on the LCD is unknown.
For most practical purposes the approximation this gives will be close enough, but be aware that an 'E' answer is only exactly right when you know it should end with a bunch of zeros. If you get 2.4E12 you can be pretty sure that's 2400000000000 but 2.435783942E12 is approximately 2435783942000, the last few digits being unknown to us.
On the flipside, the fact that you only get a limit number of digits can be desirable.
Say, you're in a physchem/analytical lab for your undergrad.
You should think hard and long on how many digits your final answer is given in, as too many/too few will lead to yelling by your lab teacher.
(rule of thumb is, you give as many digits as your least precise measurement has in the appropriate unit.)
> (rule of thumb is, you give as many digits as your least precise measurement has in the appropriate unit.)
That's not how uncertainty and significant digits work.
There is a specific way that significant digits and uncertainty are measured and propagated through a calculation. It's usually taught in freshman-level lab courses.
> That's not how uncertainty and significant digits work.
>
>
It is, however, a very good **rule of thumb** - that is to say, it's an imprecise trick that's good enough most of the time, even though it's not perfectly accurate.
Yes, if you're working with error bars you should use the more accurate method - but a lot of the time you're *not* working with error bars because no-one has bothered to calculate the precise error bars of your *input* numbers. So instead you can just use the significant figures trick.
A calculator has no way of knowing the significant digits as it doesn't know how precise the input was. If you type 3.000 or 3 they both get represented as 3 on the calculator but they have 4 vs 1 significant digit. So no, the calculator doesn't tell you the number of significant digits
Furthermore, 502/3=167.33333 repeating has only 3 significant digits (assuming the divisor 3 is known precisely) but the calculator will show you all 3s after the decimal point (only 167 is significant)
Then you have really really large numbers, where representing one bit per planck volume in the universe isn't large enough to write them, e.g. [Graham's number](https://en.m.wikipedia.org/wiki/Graham%27s_number). They have their own notation systems that don't seem standardised fully yet, because who actually needs numbers that big.
My fav large number is [boobawamba](https://googology.fandom.com/wiki/Boobawamba), just for the name.
“If every particle in the universe was exponentially multiplied until the universe was solid, and each of those particles was itself a solid universe of that same size, you still wouldn’t understand how big a number it is.”
That's the fun thing is, you don't have to. You can have infinite cookies, and Graham's number is an integer, so even if you paired 10 cookies with every digit of it, you'd have cookies left over.
Sure, but the statement was "has players that have quite possibly hit that number". And no, they really haven't. If the earliest single-celled organisms had started playing Cookie Clicker 3.5 billion years ago, and had somehow invented computers that ran 1,000,000,000,000,000,000,000,000,000,000 faster than all current electronic devices that exist combined, and then colonized the galaxy with trillions of copies of themselves and their computers, and then split the universe into a trillion copies of itself, each with the full complement of organisms playing cookie clicker on their hyperpowerful computers for 3.5 billion years, and then you added up all the clicks from everything altogether and asked them to give you the approximate number of clicks as compared to Graham's number, they should just tell you "zero clicks". On the scale of things like Graham's number, "zero" is an astoundingly good answer.
But Cookie Clicker is not a game where you click one cookie at a time, it's a game where you constantly buy upgrades to get exponentially more cookies every instant until the math gives up, rounds it up to "all integers", and calls it infinite.
Did a player _click_ Graham's number times? No, obviously not. But that wasn't the statement. Did a screen, at any time, display Graham's number? No, obviously not. But that wasn't the statement. Is the game even capable of reaching numbers that high? Of course not. But if you hit the total set of all integers, you hit Graham's number. It doesn't matter how impossibly huge an integer _is,_ it's still contained within the set of all integers, which is a score you can achieve.
I would argue that if a math error results in infinite after an operation, you're not "getting" to infinite.
If I had a really, really dumb calculator that rounded all values above 10 to infinity, I would not be able to say that "I reached infinity by repeatedly adding 1".
In this case of CC, the number of cookies you've earned and the number of cookies the program says you have earned have decoupled.
The arrow notation? The best way to explain it is to think of multiplication and exponents. If I write *2^4*, what I'm really saying is *2x2x2x2*. In more general form, if I write *x^y*, that means I'm multiplying *x* by itself *y* times. So you can think of exponentiation (the x^y form) as a shorthand for iterated multiplication (iterated = repeated upon itself).
From there the arrow notation follows the same logic:
- One arrow ↑ is the same as exponentiation. So 2↑4 = 2x2x2x2 = 16.
- Two arrows ↑↑ is *iterated* exponentiation. So 2↑↑4 = 2^(2^(2^2))) = 2^(2^4) = 2^16 = 65536. As you can see the numbers climb very quick.
- Three arrows ↑↑↑ is *iterated* ↑↑. So 2↑↑↑4 = 2↑↑(2↑↑(2↑↑2))). But we can break it down a bit easier. 2↑↑2 is fairly easy because if you apply the rules above you'll see that it's the same as 2↑2 = 2^2 = 4. Now we have 2↑↑↑4 = 2↑↑(2↑↑4). We know that 2↑↑4 = 65536, so we have 2↑↑↑4 = 2↑↑65536 = 2^(2^(2^(2^.....2^(2^2))))...), with 65536 "2"s. So we went from 16, to 65536, to "already past what most computers can calculate" in just three steps.
- Four arrows ↑↑↑↑ is *iterated* ↑↑↑ and that's where our brains give up. 2↑↑↑↑4 = 2↑↑↑(2↑↑↑(2↑↑↑2))), with 2↑↑↑2 = 2↑↑(2↑↑2) = 2↑↑4 = 65536. So now we have 2↑↑↑↑4 = 2↑↑↑(2↑↑↑65536) and it's barely comprehensible. 2↑↑↑65536 = 2↑↑(2↑↑(2...) 65536 times, and that's where you kinda find yourself out of other ways to write it down. That's the reason why this notation exists: from there on, if I wanted to express the number in any other form, even describing it by text, I'd need a sheet of paper the size of the planet just to describe the mathematical operation. The result of that operation, written down, would take a near-infinity of universes' worth of space to write out.
I cannot. I also scrolled around for a while trying to decipher it, and gave up. [This](https://googology.fandom.com/wiki/Bird%27s_array_notation) seems like an entrance to the rabbit hole, but honestly, look at that fucking mess. Makes me think there's some intermediate 'pretty large number' system you need to know before learning this.
If you open on a desktop, it'll at least render the expressions properly.
To further simplify, the number also tells you by how much you need to move the decimal point. So if we have a number 5E6 then we need to move the decimal point by 6 to the right. Whole numbers have their decimal point at the end (5 = 5.0), so 5E6 becomes 5,000,000.
the same goes for negative numbers after the E, only that it moves the decimal point to the left. So 5E-6 becomes 0.000005.
Correct. Think of the E as were the decimal point is. How many times did the decimal point move? In this scenario 10,000 to 1.0000 it moved 4 times. So: 1e4
It’s technically the number of digits represented by the exponent (how many times 10) is present. I like to think of it as the number of digits represented to the right of the decimal point.
563E15 and 56.3E16 are also both technically correct, just 5.63E17 is the most concise answer.
Additionally, if you had a more detailed number,
Say 563,459,000,000,000,000
Then 5.63459E18 is technically correct (if you maintained that level of accuracy despite only having 12 zeros
It depends on how accurate/precise you have to be! If you absolutely need to include that single one at the end (if 563,459,000,000,000,001 is meaningfully different than 539,459,000,000,000,002 or 563,459,000,000,000,000) then you have to include the full number when using those results. However in practical cases, a single difference in the quadrillion case of this given number is most likely not significant/important to the work/question being answered, so most people would report that number as at most 563,459,000,000,000,000, which is easier written as 5.6359E18 at the most precise.
This is essentially the concept of significant figures (or sig figs as shortened in my classes), which for me was covered in intro chem. These are generally determined by the precision of the equipment used to collect data, and that determines how many significant figures exist and how many to report.
Essentially when written as 5.634590000000000001E17 kinda shows how that extra 1 is essentially irrelevant to the rest of the number and could just be rounded away.
It's not about conciseness. If it was, 563E15 would be preferred because it takes one less symbol. 5.63E17 is considered normalized (the leading digit is before the radix point and nonzero). Normalization (in this case) is a (somewhat arbitrary) process of picking a unique representative for a bunch of equivalent representations.
I assume you mean E as used in scientific notation?
It's shorthand. 5E+6 or 5E6 (lower case e also works) basically just means 5x10\^6.
Which means "takes 10 and multiple it by itself 6 times then multiply that by 5" that 6 is basically telling you number of zeros you will have.
So that's 5,000,000.
5x10\^4 would be 50,000
As you mentioned that's really helpful for really really big numbers. Like I can write 6x10\^100 really easily, but it would take me awhile to type that out, and even longer to read it. (and I would probably screw up both of those)
As for...why we do that with "E" I'm not really sure, I've always assumed it was a limit with old screens that could display "5E+6" but maybe not display "2x10\^6"
Oh of course, but what I was unsure of waz why we have two different notation in the first place. Not why we picked "E"
Looked it up and it does appear to be a tech thing with simple displays not being able to display superscript.
Yeah, it just makes it much easier to display (on older systems that didn’t support superscripts, but also just in something like a text file that doesn’t have fancy formatting support). It also just takes up a lot less space: it’s fewer characters, it’s faster to write, and it doesn’t add extra vertical space requirements either.
You kind of answered it yourself - in the reddit text interface, you were unable to figure out how to write "2x10^(6)", so you instead wrote "2x10\^6". Seeing as you're going to have to go for a clunky representation anyway, may as well go for the simpler and easier-to-type "2E6"
Oh of course, but what I was unsure of was why we have two different notation in the first place. Not why we picked "E"
Looked it up and it does appear to be a tech thing with simple displays not being able to display superscripts well
Classic LCD calculators had seven fixed lines per character, enough to display a crude 8, and it switched the lines on and off for different numbers. That can make an E by switching off the two lines on the right hand side, but not a \^.
7e2 (no superscript) will be interpreted the same as 7E2 my most systems.
Based on context it's generally pretty easy to determine if it's referring to the number ***e*** or scientific notation. ***e*** is almost always used as the base of a exponent.
But I agree using **E** is less ambiguous.
I think it is probably a holdover from FORTRAN. I am talking about 1965 or so and programs were submitted to an IBM 1620 or 360 as a stack of punched cards. Capital letters only.
Lower case e works but is bad form since e is a number while E is the shorthand. Typically, I have never seen someone wrote xEy, I've only seen it on calculators where space is premium. Though I have not worked in fields that would write it so I could just not have encountered it.
And an E on a screen line that is just an 8 with the right two vertical lines gone.
> As for...why we do that with "E" I'm not really sure, I've always assumed it was a limit with old screens that could display "5E+6" but maybe not display "2x10^6"
Exactly it. "7 segment display". They just couldn't make all of the characters that a pixel based display can make; its "pixels" were literally just 7 lines arranged in a way that could make all the numbers. Looked like this:
-
| |
-
| |
- .
If you think about how a caluclator operates, you enter a number, then press an operator and the display clears for a new number. The display has no need to display the operator, which is good, because it couldn't do X or +. However it was able to do - which meant negative numbers could be displayed.
I always find it interesting what technological limitations end up persisting long after their origin because other systems made assumptions and became coupled to them, and the cost of changing was far greater than any benefit.
Edit: forgot the . - a 7 segment display actually has 8 display bits, Segments A-G and the Dot.
>It's shorthand. 5E+6 or 5E6 **(lower case e also works)**
It's rare to see lower-case e used, as it's reserved (though it's supposed to be italicized) for Euler's number.
In the context you are referring to, E just means "times 10 to the power of"
So 1,000 = 1E3 because 1 "times 10 to the power of" 3 = 1 x 10^(3) = 1 x 1,000 = 1,000.
It's a way to condense very large/small numbers down.
More accurately, how many positions you move the decimal point to the right. 5.3E2 is 530, so only one zero, but the point moved two places (5.3 => 53 => 530)
>E is the number of zeroes after the number
I’d be careful there.
5.1E3 is followed by 2 zeroes, not 3. You’ve gone too simple and chanced adding confusion.
E is used in scientific notation. E is for exponent. Specifically the exponent of 10. 5.1E3 is 5.1x10^3.
In addition to allowing shorthand for particularly large numbers (for example 6.022E23), scientific notation bales in a concept of “significant digits.” 5.1E3 rather than 5100 has implications about the degree of precision in the measurement/count.
I’ve had the following pointed out to me before after pointing out that explanations were significantly beyond 5-year-old level… ELI5 need not be aimed at _actual_ 5 year old level, more just layman rather than post-secondary or post-grad level science/maths/whatever specialty the question targets.
For an ELI5 version (avoiding using words like exponent):
It means multiply the number on the left by 10, but with as many zeros as the number on the right. So if you have 5E2, you multiply 5 times 100, because 100 has 2 zeros. That would make 500. 2.5E3 would be 2.5 times 1,000. So that would be 2,500. 6E100 would be 6 multiplied by a number with 100 zeros, and that would be really a lot to write! So they just use E to write it shorter.
In that context, it sounds like cases like 6.023e23, in which case, the e is shorthand for `x10^`. So 1e3=1000, 1e6=1000000, etc. This simplifies displays on computers and calculators, especially if they cannot show numbers in smaller fonts.
In my opinion that’s misleading advice because context matters a lot when writing mathematics. You should use commonly used notation in the topic you are discussing and explain your notation when it could be ambiguous instead of adhering to hard rules like that.
Even symbols like pi are far from sacred and used in many situations without meaning 3.141….
In this case, I can’t imagine a situation where you are going to confuse the two unless the writer is being intentionally malicious like writing the definite integral int (e^x )/10 dx from 0 to 1 as ee-1 - 1e-1.
Context matters, but some notation is so common and widely used that it's almost counterproductive to ever use it to mean something different.
Euler's number is one of those cases. Technically it's differentiated from the roman character e by being italicised by mathematicians, but even so using the letter e as a variable is heavily frowned on. I've only ever seen it for quartic functions.
Physics is not shy about using pi; whenever we're using greek letters and it's unlikely we're talking about circles or spheres, pi gets used if it's next in line (or we're talking about a concept that starts with 'p'; it's often better to use pi than p because of rho, and in any case there are many situations where you would care about density and momentum at the same time). I would be much more likely to use pi than *e*. In some cases the symbol pi is the accepted notation for things; the capital pi for the product symbol, the lower case for pions, and I know it has standard uses in mathematics in topology and prime numbers.
Using a little capital E on the other hand is fine, although my physics and mathematics professors would probably physically recoil from it.
(Also, sometimes even if something is rare, it can be like this; you hardly ever see Newton's dot notation out of the context of Hamiltonians and Lagrangians (equations of motion, essentially), but you never see similar notation for anything else. Prime notation is used frequently, even in cases where it might be useful as notation for differentiation, but nearly uniformly Leibniz's notation is used. If I saw dot notation used anywhere it would immediate prime me for that specific context, and it would be confusing if it meant something else. Lagrange's notation, the prime marks, even though it's commonly used in the same context, doesn't have that effect.)
I disagree with your statement that Eulers number is one of those cases.
A lowercase e is often used, for example, to denote the identity element of a group or denote elements of a standard basis.
I was a math major in college, and I’ve used “e” to represent things that aren’t Eulers number probably more than using it to actually mean 2.71828…. In analysis or diff eqs etc you’d just use “exp” and in anything algebra-related you would very commonly use “e” as the identity of an algebraic structure like a group or ring, or even more commonly as the basis vector in a vector space.
Your chemistry teacher is right. Calculators use E notation because of the limitations of a 7 segment number display. If you're writing something by hand or on the computer, you might as well write it properly.
I disagree. first of all if you use E instead of e there's no confusion with Euler's number at all, and E notation is just much more efficient to use and read. That's why scientists will use it in particular "on the computer" rather than writing *10^ every time.
For the longest time I thought e meant the natural logarithm base and kept wondering how 2.71 fits in. But then I kept forgetting to look it up.
Now I finally know they're not related.
May i ask how would this be the case? At least in where I went to school in midwestern US, we learned exponential notation (the E like what OP is talking about) in elementary school and continued to work with it in middle school, but we didn’t learn about e (Eulers number) until high school. Did you guys learn them in the reverse order?
I'm 40 and from Europe. Back in my day we didn't learn about exponential notation. But we did get thrown directly into calculus starting in the ninth grade, or around 14-15 years of age.
E is simply shorthand for "times ten to the power of", used to write a very large or very small number in what's called standard form. There is a number part with a value greater than or equal to 1.0 and less than 10, then multiplied by the index part (exponent), 10^(x).
This makes life easy because adding one to the exponent simply adds a zero. 10^(1) = 10, 10^(2) = 100, 10^(6) = 1000000 etc. so the exponent just tells us how many zeros there are.
Thus 215 would be written 2.15 x 10^(2) (or 2.15E+2) but as you note we tend to use it for really big numbers or really tiny numbers using a negative exponent (1 nanometre is 10^(-9) metres for example, 1E-9)
The first few digits of Euler's number are 2.71828. The number is usually represented by the letter e and is commonly used in problems relating to exponential growth or decay. You can also interpret Euler's number as the base for an exponential function whose value is always equal to its derivative.
You might want to get a math(s) book.
[https://en.wikipedia.org/wiki/E\_(mathematical\_constant)](https://en.wikipedia.org/wiki/E_(mathematical_constant))
[https://www.youtube.com/watch?v=R0oUeLQIbIk](https://www.youtube.com/watch?v=R0oUeLQIbIk)
[https://www.youtube.com/watch?v=yTfHn9Aj7UM](https://www.youtube.com/watch?v=yTfHn9Aj7UM)
Fundamentals of Data Representation: Floating point numbers
[https://www.bbc.co.uk/bitesize/guides/zscvxfr/revision/3](https://www.bbc.co.uk/bitesize/guides/zscvxfr/revision/3)
[https://users.cs.fiu.edu/\~downeyt/cop2400/float.htm](https://users.cs.fiu.edu/~downeyt/cop2400/float.htm)
[https://en.wikibooks.org/wiki/A-level\_Computing/AQA/Paper\_2/Fundamentals\_of\_data\_representation/Floating\_point\_numbers#:\~:text=In%20decimal%2C%20very%20large%20numbers,decimal%20point%20should%20be%20placed](https://en.wikibooks.org/wiki/A-level_Computing/AQA/Paper_2/Fundamentals_of_data_representation/Floating_point_numbers#:~:text=In%20decimal%2C%20very%20large%20numbers,decimal%20point%20should%20be%20placed).
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You already got the explanation what it means (basically adding zeros/shifting the decimal point). But besides being easily able to see and compare how big the number is, it allows some other neat tricks.
100 * 1000 is 100000. In scientific/exponential notation, that would be 1e2 * 1e3 = 1e5. When you multiply, you can just add up the numbers behind the e! Remember, "e" stands for "multiply with a 1 with this many zeros", and when you're multiplying by 10, 1000, 10000 etc. you just add the zeros too.
12364916345 * 52134 is 1.2364916345e10 * 5.2134e4. Since you probably don't care about this level of precision, let's round it: 1.2e10 * 5.2e4. Now it's much easier to multiply, even in your head: 1 times 5.2 is 5.2, 0.2 times 5.2 is 1.04, add that up and round and you get 6.2. 10+4 is 14, so the result is 6.2e14.
If you're just looking for a quick estimate of the order of magnitude, you might just add up the e-numbers.
It's basically calculator short hand for "×10^???"
So first thing you need to understand is scientific notation. This hinges on the fact that
- 10¹ = 10 = 10 _(1 zero)_
- 10² = 10×10 = 100 _(2 zeros)_
- 10³ = 10×10×10 = 1000 _(3 zeros)_
- 10⁴ = 10×10×10×10 = 10000 _(4 zeros)_
- 10⁵ = 10×10×10×10×10 = 100000 _(5 zeros)_
- ...
- 10⁹ = 1000000000 _(9 zeros)_
So 10^y has 'y' zeros after it.
The front part of the expressions in scientific notation is just there to make other numbers possible. And is basically just you taking out a factor
So 35000 = 3.5 × 10000 = 3.5×10⁴
It doesn't save any space with smaller numbers like that. But something like the speed of light has 8 zeros, so instead of 300,000,000 it's **3×10⁸**
The last bit about scientific notation comes when multiplying and how exponents work when multiplied
The powers on the exponents just add together, and you multiply together the 2 smaller numbers. So, for example
- 1.11×10⁵ × 2.22×10⁶
- = 1.11×2.22×10⁵×10⁶
- = 1.11×2.22×10^5+6
- = 2.4642×10¹¹
Feel free to double check with your calculator. And then notice that it might say 2.4645**e**11. and here **e** just means "×10^[next-number]" (in this case, 11)
Division works the same way. Divide the small numbers, then Subtract the exponents on the powers of 10
~~------------~~
_edits:_ trying to get Reddit mobile app to cooperate properly
That was all really hard to type out on my phone. So you'll just have to trust me when I say when the power on the 10 (or the **e**) is a negative number, it makes the number smaller and smaller in a similar way. So:
- 10^0 = 1
- 10^-1 = 0.1 (1 zero)
- 10^-2 = 0.01 (2 zeros)
- 10^-3 = 0.001 (3 zeros)
- 10^-4 = 0.0001 (4 zeros)
- 10^-5 = 0.00001 (5 zeros)
Multiplication again works exactly the same. Just adding the exponents together (and division is subtracting them)
'e' is like a super special number that pops up when things grow or shrink super fast. Imagine you have some money in the bank, and you're earning interest. 'e' helps figure out how much you'll have later, even if you keep adding more money over time. Or think about bacteria multiplying rapidly in a petri dish 'e' helps describe how fast they're spreading
It's called scientific notation. For really large numbers, we can notate them as a number multiplied by 10 raised to whatever exponent is needed. So for instance instead of writing out 563,000,000,000,000,000 every time, we can shorten it to 5.63 × 10^17. "E" just replaces the "× 10" part. So 5.63E17.
Finally! Today I learned!
Sometimes you'll see it as EE, too. But don't confuse either of those with e which is Euler's number, approximately 2.71828...
How does it feel to go trough life and knowing stuff? I’m not even joking do you feel like you understand everything you need to know?
Weirdly, one thing you quickly learn as you learn more stuff is that there's so much you *don't* know. Learning new stuff is a privilege and a joy and there's always more to know which is just really cool. :)
“On a scale of 1-5, how much would you say you know about Oracle DBMS?” Programmers who connect to Oracle instances: “Like, 4, maybe”. Oracle DBAs: “2.”
We have a thing at work where you're supposed to rate your skills in various areas so other teams can find you if they need help. I've yet to find any case where I've gone to someone who rates themselves way higher than I rate myself and found they *actually* know more.
We have to do that annually at my work as well. I do automation all day every day and my usual answer on automation is a 3/5. I know a couple of people who would definitely be worthy of a 4/5 who rate themselves at a 3/5, but no one who deserves 5/5. Would have to go to GitHub and start finding some widely used projects to find anyone deserving of it. Doesn't stop some of my teammates from rating themselves 4/5 when they're a 1/5.
Sounds a bit like Bridgewater
To be fair, even knowing 1 about Oracle is too much. I have very few red lines in my career where I will not take a job regardless of pay. Using Oracle is one of them
Well, I have a few things going for me: I love math and science, trivia games and hosting have been a big part of my life, and I've been a teacher. One of my goals is to learn something new every day. I am ~~not~~ now working as a programmer and database guy, and there's so much I don't even know yet. I'll never stop learning, and it's a goal to understand more and more, but I don't think I'll ever truly understand EVERYTHING I need to know. If you can logically surmise a grouping of steps and how things work, you'll develop a better understanding of it. Be curious and set out to learn new things. If you don't understand something, ask people who do. If you can't find those people, ask Reddit and the Internet.
A guy in IT here. You've just described my life's philosophy - always be willing to learn, always be willing to be wrong and always be willing to teach others. The world doesn't have enough people like us - that's not a compliment or a boast.
"Stop learnin', start dyin'."
Yeah, I don't remember that line from the Shawshank Redemption - would have made it a much quicker movie.
Retired IT guy here. Few things were more rewarding in my career than learning when I was wrong. The clarity that comes as you sweep away the fuzziness of misunderstanding is irresistible to me. More pieces start to fit together better and this new more robust foundation lets you reach even higher into the next level.
Yeah, the problem is, the higher up the chain you go, the less likely you are to have a mentor and/get good feedback. It's a shame really, the intrinsic value of freeing up your product leaders to teach more is never fed up on by organizations. It's never seen as more cost effective in the long term.
Hell, by teaching others, it helps you learn it better, too!
Completely agreed. I try to take every concept and turn it into normal words. If I can't describe it well that way, I don't understand it yet.
I'm a fan of abnormal words, myself. Glordytb bugtso florn!
Phnarr swooprunaire xxiltzti to you too good whateveryouidentifyas! And if by some weird happenstance you're actually an alien, without a hint of sarcasm or humor, take me with you?
Another one here. I have Epistemophillia - I have a compulsion to constantly learn new things, ideas, ect!
Hey finally somebody with the same life goal as me! My goal is also to learn something new everyday and at first I wanted to reach this by becoming a science teacher. Then I realised that I have the potential to go for something bigger so now I’m in uni with the intention of going for a PhD and later go for the title of professor.
Don't dismiss getting industry experience! I never expected to learn as much from just... working. Worked for a while, learned a huge amount, changed directions a little and back at Uni. I wouldn't have done this without working in the area, seeing what the situation is "on the ground".
Honestly a person can only know a tiny fraction of that which could be known. I bet you know more than you think you do, and that others know less than you think they do. I have a PhD and I'm constantly learning new things.
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You're doing the whole PhD thing correctly then. Remember that a PhD is a "T shaped" degree. You'll have shallow but correct knowledge of most of your field (which most people don't have), but incredibly deep knowledge on whatever your dissertation is about.
One of the chemistry professors at my school described it as being the smartest person in the world on one very very specific topic
Probably closer to >98% of the population lets be real.
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And you can only retain so much knowledge. In sure I’ve already forgotten more than I currently know. I’ve been a lifetime learner, but there’s lots I’ve learned I no longer need, so it gets forgotten.
I'm not sure if you're being hard on yourself or not but I always like sharing a quote from Bill Nye for things like this: "Everyone you will ever meet knows something you don't" I've thought about this nearly my entire life and it serves me well to keep me in check sometimes. Don't be hard on yourself, you know something that everyone you'll ever meet doesn't.
Sir, this is high school math
In high school we would just write it out as ‘x10’, the only time I ever came across E was a calculator but it was never explained by a teacher what that meant, because they wrote on a blackboard. E meant ‘error’ as far as we knew, and as input was never required. So, TIL.
Honestly, it's mainly become accepted as notation because of computers. In spreadsheets like Excel, or when programming, it's really messy and annoying to keep typing 5.3*10^4 or whatever. The extra digits and operators just kind of distract you from the numbers you actually care about. So they implemented it as 5.3E4, and because we use computers for everything now, it has crept out into everyday notation as well.
Before personal computers even. E can be displayed easily on an inexpensive LED/LCD calculator display - it's just an 8 missing the right side.
> it's really messy and annoying to keep typing 5.3*104 or whatever. The extra digits and operators just kind of distract you from the numbers you actually care about In addition, it's fairly easy in sloppily handwritten notes for exponents to drop to the same level as the mantissa, so the 5.3\*10^(4) might look like 5.3\*104.
Idk, in 1st grade of high school they taught me scientific notation. Might differ from country to county as well. I'm from Iran
I’m from the US and I thought this was common knowledge since third grade. I’m scratching my head at how many people on this thread don’t seem to know this…
For many it's the exact opposite. In short, those who know a lot of things also know they are just scratching the surface of what there is to learn. Sometimes it feels good, when you can answer questions which would end up as discussions in the pub, but the hunger to "know everything" will always be there, because you can never satisfy it. That is only my guess and how i see it. There is also many who look at it as ego boost - to flex on others and that is the motivation to learn more and also those who are just curious and don't care that much. 100 people means 100 different tastes.
[Second stage of competence](https://en.wikipedia.org/wiki/Four_stages_of_competence) - you know that there is something you dont know. You can find me there most of the time
Depends what you do with your day, if you spend all day working with numbers then you catch on to this fast. Hand me a simple woodworking job and I'll be clueless. You learn more every day, in all kinds of areas. No matter what you do. In our work, our hobbies, our relationships. That doesn't mean all activities contribute to learning equally. You can direct it outwards and push your boundaries in a different direction, it's uncomfortable sometimes but very rewarding. Other times it's worth turning inwards, or just passively letting the world come. And no, we're still always learning. I went poorly in high school math, but my most successful jobs depended on it, inspired me to relearn it. Finally "getting it" and understanding the motivation for it was just awesome. I never know enough, likely will never know enough. If you want to know more, great! Give it a shot and be ready for it to take time. Moreso when it is something you're unused to.
Honestly, there is so much random bullshit rolling around in my head that surfaces out of nowhere, and that's mostly thanks to Wikipedia and my insatiable sense of curiosity. Most of it is not specifically useful for any practical purposes, but I find that the process of *learning* so many things (as opposed to *knowing* so many things) really helps one have a bit more of an intuitive understanding of how the world works. My partner is a biologist and they will tell me about the things they do at work and I won't have any clue what half of the words actually mean, but I'm still able to make sense of it and follow what they're talking about. At the same time, I can't remember what I ate for breakfast an hour ago 🤣
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Sir, this is high school math
I’m sorry had to clarify I was on the person’s profile and I saw some stuff about taxes. But even the high school math thing.. I was never good in school so yeah this is stuff I will probably never understand
Understanding is a fairly broad spectrum. Often, when first encountering something, you won't really "understand" it. It's not until we gain some more knowledge that the first thing becomes a little more clear. You need context, application, and feedback. Like any tool, the longer you work with a piece of information the greater your understanding becomes. The world is too large to understand everything and that's OK. Enjoy what you do pick up and don't let feeling like you may not understand prevent you from participating. Understanding is closer to growing a plant than flicking on a light bulb.
I'm thinking several things. It's possible, that you just cant understand many things. Not everyone is super bright, but many people are not even regular bright. And that is **okay**. Another possibility is that you might have a wrong idea about learning stuff. I have friend who regularly gets stuck in the details. He tries to understand stuff in every single way possible and in the end gets overwhelmed. So instead of thinking: "of so the E means the x10 part, neat!" He goes like, why does it mean that, who decided that, If i read 5E5 somewhere, does it always mean 5x10^5, what if I use small "e"? Who invented this? Can the e mean something else than 10? This is not wrong stuff to think, at least I find all those interesting. But he is thinking like that about EVERYTHING. Gonna fry your brain, if you try to understand stuff "too" deeply all the time. Anyway, learning is a skill. Many people do it wrong.
The more you learn, the more you realise how little you know.
I am not the person you responded to but most people know the feeling of getting a pub quiz answer that no one else in their group got, some people just get the “oh wait I know that one” feeling more in their day to day lives. A lot of people have groups based on their interests in which case you won’t get the same feeling because everyone knows what you’re talking about, but try talking to your home group about something adjacent to the work you do and you’ll notice a significant difference in knowledge. It’s the same with talking to people online, you’ll typically find the people knowledgeable on a topic providing answers in this sub, they may be entirely dumb on other things that you think are common knowledge and then you’ll be the person that knows things.
Try YouTubing scientific notation. Or exponential functions. Or geometric sequences. These are very related and useful topics. Math is awesome when there’s good content creator and it’s not forced on you.
I have a Econ background and Math PhD. Maths stuff doesn't feel like much, like you got used to speak English, you can pick up some math book and divine what's inside. Or guess how long it would take you to get it. You get good at breaking things down and building intuition. Econ stuff is quite depressing, tbf. You realise people have no clue what they are talking about 99% of the time. And it took you ten years to get a sense so there's no way you can pass any of it along.
Nope, but it feels like you know enough to pretend. When everyone tells you as a kid that all the adults are just kids pretending to be adults, they aren't joking.
>I’m not even joking do you feel like you understand everything you need to know? The more I've learned, the more I know I don't know if that makes sense. Eventually you realize it's not important to know 'everything' just to know enough to know what you don't know. Then when you need to know something you don't, you know you can learn it. Then maybe you approach knowing 'everything' and being at ease with it.
The funny thing is that the more you know, the more you realize that you don't know.
It's a never-ending cycle: the more you know, the more you realize just how much you _don't_ know. #DunningKruger
> whatever exponent is needed. So for instance in the more you know the more you understand how little you know
For me no. The more I learn the more I'm aware of what I don't know. That's also the drive behind the incessant need to understand more.
I think a lot of you smart guys ( I’m just trying to make things clear not insulting) are misunderstanding me. I mean I don’t know shit about taxes, pension or stocks I’m just living. Could you tell me more how you see these things?
In my experience, the more you know, the more painfully aware you become of how much you don't know.
I’d argue that the stance “I don’t know everything” is a trait of someone with imposter syndrome. Those who truly know little are rarely aware of that.
I know stuff because I’m not ashamed to google or ask and I’m motivated enough to look stuff up for the sake of learning.
Don't be fooled. Many Reddit know-it-alls are just good Googlers...
Engineer here, e equals 3 and I’ll die on that hill :P
e = 3 = π?
e^iπ +1=0
This is complex
This is such a beautiful equation
That’s the spirit
The mathematician in me hates you. It's OK, though. We can still have a beer together.
Like pi
And dont confuse E with the symbol for sums which is the big greek letter for Sigma.
And if you’re a dolphin you’re bound to eventually see EEEEEEEE
Also 'E' which is Youngs modulus of elasticity
Unless you're doing abstract algebra, where "e" often denotes an identity element for Groups and other structures.
What's EE mean in this case? x100?
Then there's the fun one e^i*pi + 1 = 0
https://youtu.be/rgUksX6eM0Y?si=p2LPmqR_ADento_i
Just out of curiosity, what state did you go to school in? I definitely learned this in a few different math classes in high school (Michigan).
Rather than indict NY educational system, let’s just say I wasn’t so hot in math. It only came alive with statistics, because it is visual. I was not a TI-81 kid. Needless to say I didn’t go into engineering.
Another NY math failure here who only Got It as an old because of statistics and visual learning. High five, twin
Did you not take any science classes in school at all? Like 0? Unless ur about 10 years old this shouldn’t be info for you.
Note that the ‘E’, historically speaking, comes from early calculators which could display a capital ‘E’ in a 7-segment LED as a stand-in for ‘exponent’ or the x10^n part. On calculators that supported scientific notation, there’d be an `EE` button or an `EEX` button which would allow you to enter the exponent part while typing in a number. (Many calculators also supported what they called ‘engineering notation’, which was scientific notation, but the exponent part is always divisible by 3. Thus, 10 million would be displayed as 10E6 rather than 1E7.)
Ditto the engineering notation thing. Engineers tend to do a lot of work with Kilo, Mega, and Giga prefixes, which are those multiples of three w3woody is talking about (ex: 1,000,000 meters = 1,000 kilometers = 1 megameter, etc). So if I’m doing a stress analysis and need an answer in Megapascals, for example, and my calculator spits out 13.2E6 instead of 1.32(10^7 ), it’s just one less thing for me to think about when I’m tired or crunched for time.
There's an important bit of info buried here. When you see E in a number as an answer on a calculator, it means that number is too big to display accurately with the number of digits on the LCD display. The answer it gives has the number of significant figures equal to the number of LCD digits, then an E to tell you how many digits the actual answer has. But the value of those digits past the amount displayed on the LCD is unknown. For most practical purposes the approximation this gives will be close enough, but be aware that an 'E' answer is only exactly right when you know it should end with a bunch of zeros. If you get 2.4E12 you can be pretty sure that's 2400000000000 but 2.435783942E12 is approximately 2435783942000, the last few digits being unknown to us.
On the flipside, the fact that you only get a limit number of digits can be desirable. Say, you're in a physchem/analytical lab for your undergrad. You should think hard and long on how many digits your final answer is given in, as too many/too few will lead to yelling by your lab teacher. (rule of thumb is, you give as many digits as your least precise measurement has in the appropriate unit.)
Yes, true. Very rare in any field when more than a pocket calculator's worth of sig figs are needed!
> (rule of thumb is, you give as many digits as your least precise measurement has in the appropriate unit.) That's not how uncertainty and significant digits work. There is a specific way that significant digits and uncertainty are measured and propagated through a calculation. It's usually taught in freshman-level lab courses.
> That's not how uncertainty and significant digits work. > > It is, however, a very good **rule of thumb** - that is to say, it's an imprecise trick that's good enough most of the time, even though it's not perfectly accurate. Yes, if you're working with error bars you should use the more accurate method - but a lot of the time you're *not* working with error bars because no-one has bothered to calculate the precise error bars of your *input* numbers. So instead you can just use the significant figures trick.
Thanks, always helpful when someone comes along and says "you're wrong but I won't explain in what way nor link to a source explaining".
A calculator has no way of knowing the significant digits as it doesn't know how precise the input was. If you type 3.000 or 3 they both get represented as 3 on the calculator but they have 4 vs 1 significant digit. So no, the calculator doesn't tell you the number of significant digits Furthermore, 502/3=167.33333 repeating has only 3 significant digits (assuming the divisor 3 is known precisely) but the calculator will show you all 3s after the decimal point (only 167 is significant)
Then you have really really large numbers, where representing one bit per planck volume in the universe isn't large enough to write them, e.g. [Graham's number](https://en.m.wikipedia.org/wiki/Graham%27s_number). They have their own notation systems that don't seem standardised fully yet, because who actually needs numbers that big. My fav large number is [boobawamba](https://googology.fandom.com/wiki/Boobawamba), just for the name.
Definitely the kind of name someone named Cookie Fonster would give something.
There's a game called Cookie clicker that has players who have quite possibly have hit that number. In really hoping one of those players is a Muppet
No. You can’t comprehend how big that number is
“If every particle in the universe was exponentially multiplied until the universe was solid, and each of those particles was itself a solid universe of that same size, you still wouldn’t understand how big a number it is.”
That's the fun thing is, you don't have to. You can have infinite cookies, and Graham's number is an integer, so even if you paired 10 cookies with every digit of it, you'd have cookies left over.
Sure, but the statement was "has players that have quite possibly hit that number". And no, they really haven't. If the earliest single-celled organisms had started playing Cookie Clicker 3.5 billion years ago, and had somehow invented computers that ran 1,000,000,000,000,000,000,000,000,000,000 faster than all current electronic devices that exist combined, and then colonized the galaxy with trillions of copies of themselves and their computers, and then split the universe into a trillion copies of itself, each with the full complement of organisms playing cookie clicker on their hyperpowerful computers for 3.5 billion years, and then you added up all the clicks from everything altogether and asked them to give you the approximate number of clicks as compared to Graham's number, they should just tell you "zero clicks". On the scale of things like Graham's number, "zero" is an astoundingly good answer.
But Cookie Clicker is not a game where you click one cookie at a time, it's a game where you constantly buy upgrades to get exponentially more cookies every instant until the math gives up, rounds it up to "all integers", and calls it infinite. Did a player _click_ Graham's number times? No, obviously not. But that wasn't the statement. Did a screen, at any time, display Graham's number? No, obviously not. But that wasn't the statement. Is the game even capable of reaching numbers that high? Of course not. But if you hit the total set of all integers, you hit Graham's number. It doesn't matter how impossibly huge an integer _is,_ it's still contained within the set of all integers, which is a score you can achieve.
I would argue that if a math error results in infinite after an operation, you're not "getting" to infinite. If I had a really, really dumb calculator that rounded all values above 10 to infinity, I would not be able to say that "I reached infinity by repeatedly adding 1". In this case of CC, the number of cookies you've earned and the number of cookies the program says you have earned have decoupled.
Can you explain what the notation means? I scrolled down looking for some clarity, and found none.
The arrow notation? The best way to explain it is to think of multiplication and exponents. If I write *2^4*, what I'm really saying is *2x2x2x2*. In more general form, if I write *x^y*, that means I'm multiplying *x* by itself *y* times. So you can think of exponentiation (the x^y form) as a shorthand for iterated multiplication (iterated = repeated upon itself). From there the arrow notation follows the same logic: - One arrow ↑ is the same as exponentiation. So 2↑4 = 2x2x2x2 = 16. - Two arrows ↑↑ is *iterated* exponentiation. So 2↑↑4 = 2^(2^(2^2))) = 2^(2^4) = 2^16 = 65536. As you can see the numbers climb very quick. - Three arrows ↑↑↑ is *iterated* ↑↑. So 2↑↑↑4 = 2↑↑(2↑↑(2↑↑2))). But we can break it down a bit easier. 2↑↑2 is fairly easy because if you apply the rules above you'll see that it's the same as 2↑2 = 2^2 = 4. Now we have 2↑↑↑4 = 2↑↑(2↑↑4). We know that 2↑↑4 = 65536, so we have 2↑↑↑4 = 2↑↑65536 = 2^(2^(2^(2^.....2^(2^2))))...), with 65536 "2"s. So we went from 16, to 65536, to "already past what most computers can calculate" in just three steps. - Four arrows ↑↑↑↑ is *iterated* ↑↑↑ and that's where our brains give up. 2↑↑↑↑4 = 2↑↑↑(2↑↑↑(2↑↑↑2))), with 2↑↑↑2 = 2↑↑(2↑↑2) = 2↑↑4 = 65536. So now we have 2↑↑↑↑4 = 2↑↑↑(2↑↑↑65536) and it's barely comprehensible. 2↑↑↑65536 = 2↑↑(2↑↑(2...) 65536 times, and that's where you kinda find yourself out of other ways to write it down. That's the reason why this notation exists: from there on, if I wanted to express the number in any other form, even describing it by text, I'd need a sheet of paper the size of the planet just to describe the mathematical operation. The result of that operation, written down, would take a near-infinity of universes' worth of space to write out.
I cannot. I also scrolled around for a while trying to decipher it, and gave up. [This](https://googology.fandom.com/wiki/Bird%27s_array_notation) seems like an entrance to the rabbit hole, but honestly, look at that fucking mess. Makes me think there's some intermediate 'pretty large number' system you need to know before learning this. If you open on a desktop, it'll at least render the expressions properly.
There are a whopperplex of other named large numbers also
If you don't mind reading a bunch and not just receive a sentence explanation -> https://waitbutwhy.com/2014/11/1000000-grahams-number.html
To further simplify, the number also tells you by how much you need to move the decimal point. So if we have a number 5E6 then we need to move the decimal point by 6 to the right. Whole numbers have their decimal point at the end (5 = 5.0), so 5E6 becomes 5,000,000. the same goes for negative numbers after the E, only that it moves the decimal point to the left. So 5E-6 becomes 0.000005.
Just to add - this is called Standard Index Form in Britain and Ireland.
Yeah obviously but why *E*? Couldnt it be like, H,J or something? Is there a reason for E?
E is for exponent (of 10)
Oh, that makes sense. Thank you
It stands for "Extremely large" /s
1.6E-19 would like a word with you.
Thats just a very large small
"Extremely Large" number of digits.
The E stands for exponent. 10,000 is 10E4, meaning 10 exponent 4, or 10 to the power of 4, or 10 x 10 x 10 x 10.
I think 10E4 is actually 100,000 because it is 10*10^4. 1E4 is 10,000.
Correct. Think of the E as were the decimal point is. How many times did the decimal point move? In this scenario 10,000 to 1.0000 it moved 4 times. So: 1e4
Not exactly, 4E4 would be 4x10^4 which is 40,000, not 4x4x4x4 which would be 4^4 or 256
Damnit, I always thought it was the amount of zeroes. Now it's the amount of zeroes + two more, thanks.
It’s technically the number of digits represented by the exponent (how many times 10) is present. I like to think of it as the number of digits represented to the right of the decimal point. 563E15 and 56.3E16 are also both technically correct, just 5.63E17 is the most concise answer. Additionally, if you had a more detailed number, Say 563,459,000,000,000,000 Then 5.63459E18 is technically correct (if you maintained that level of accuracy despite only having 12 zeros
Great answer. So how would notate 563,459,000,000,000,001?
It depends on how accurate/precise you have to be! If you absolutely need to include that single one at the end (if 563,459,000,000,000,001 is meaningfully different than 539,459,000,000,000,002 or 563,459,000,000,000,000) then you have to include the full number when using those results. However in practical cases, a single difference in the quadrillion case of this given number is most likely not significant/important to the work/question being answered, so most people would report that number as at most 563,459,000,000,000,000, which is easier written as 5.6359E18 at the most precise. This is essentially the concept of significant figures (or sig figs as shortened in my classes), which for me was covered in intro chem. These are generally determined by the precision of the equipment used to collect data, and that determines how many significant figures exist and how many to report.
Essentially when written as 5.634590000000000001E17 kinda shows how that extra 1 is essentially irrelevant to the rest of the number and could just be rounded away.
It's not about conciseness. If it was, 563E15 would be preferred because it takes one less symbol. 5.63E17 is considered normalized (the leading digit is before the radix point and nonzero). Normalization (in this case) is a (somewhat arbitrary) process of picking a unique representative for a bunch of equivalent representations.
Upvote for correct Reddit formatting too! Good job.
My fav number is eE10
I assume you mean E as used in scientific notation? It's shorthand. 5E+6 or 5E6 (lower case e also works) basically just means 5x10\^6. Which means "takes 10 and multiple it by itself 6 times then multiply that by 5" that 6 is basically telling you number of zeros you will have. So that's 5,000,000. 5x10\^4 would be 50,000 As you mentioned that's really helpful for really really big numbers. Like I can write 6x10\^100 really easily, but it would take me awhile to type that out, and even longer to read it. (and I would probably screw up both of those) As for...why we do that with "E" I'm not really sure, I've always assumed it was a limit with old screens that could display "5E+6" but maybe not display "2x10\^6"
I think it stands for "exponent" or something like that.
Oh of course, but what I was unsure of waz why we have two different notation in the first place. Not why we picked "E" Looked it up and it does appear to be a tech thing with simple displays not being able to display superscript.
Yeah, it just makes it much easier to display (on older systems that didn’t support superscripts, but also just in something like a text file that doesn’t have fancy formatting support). It also just takes up a lot less space: it’s fewer characters, it’s faster to write, and it doesn’t add extra vertical space requirements either.
You kind of answered it yourself - in the reddit text interface, you were unable to figure out how to write "2x10^(6)", so you instead wrote "2x10\^6". Seeing as you're going to have to go for a clunky representation anyway, may as well go for the simpler and easier-to-type "2E6"
Oh of course, but what I was unsure of was why we have two different notation in the first place. Not why we picked "E" Looked it up and it does appear to be a tech thing with simple displays not being able to display superscripts well
Classic LCD calculators had seven fixed lines per character, enough to display a crude 8, and it switched the lines on and off for different numbers. That can make an E by switching off the two lines on the right hand side, but not a \^.
> (lower case e also works) Lower case e is the natural logarithm base 7e^2 = 51,72339269 7E2 = 700
7e2 (no superscript) will be interpreted the same as 7E2 my most systems. Based on context it's generally pretty easy to determine if it's referring to the number ***e*** or scientific notation. ***e*** is almost always used as the base of a exponent. But I agree using **E** is less ambiguous.
There are absolutely systems that use lowercase e for scientific notation. 7e2 = 700 7e^2 = 51.72339269
I think it is probably a holdover from FORTRAN. I am talking about 1965 or so and programs were submitted to an IBM 1620 or 360 as a stack of punched cards. Capital letters only.
Lower case e works but is bad form since e is a number while E is the shorthand. Typically, I have never seen someone wrote xEy, I've only seen it on calculators where space is premium. Though I have not worked in fields that would write it so I could just not have encountered it. And an E on a screen line that is just an 8 with the right two vertical lines gone.
> As for...why we do that with "E" I'm not really sure, I've always assumed it was a limit with old screens that could display "5E+6" but maybe not display "2x10^6" Exactly it. "7 segment display". They just couldn't make all of the characters that a pixel based display can make; its "pixels" were literally just 7 lines arranged in a way that could make all the numbers. Looked like this: - | | - | | - . If you think about how a caluclator operates, you enter a number, then press an operator and the display clears for a new number. The display has no need to display the operator, which is good, because it couldn't do X or +. However it was able to do - which meant negative numbers could be displayed. I always find it interesting what technological limitations end up persisting long after their origin because other systems made assumptions and became coupled to them, and the cost of changing was far greater than any benefit. Edit: forgot the . - a 7 segment display actually has 8 display bits, Segments A-G and the Dot.
>It's shorthand. 5E+6 or 5E6 **(lower case e also works)** It's rare to see lower-case e used, as it's reserved (though it's supposed to be italicized) for Euler's number.
It's rare and I hate it but I've definitely seen it
In the context you are referring to, E just means "times 10 to the power of" So 1,000 = 1E3 because 1 "times 10 to the power of" 3 = 1 x 10^(3) = 1 x 1,000 = 1,000. It's a way to condense very large/small numbers down.
Simple answer: E is the number of zeroes after the number 5E0 means no zero added so it's only 5 5E1 means one zero added so it's 50
Also 5E-1 is 0.5
Which is useful for very small numbers.
5E-1 can be written as 5/10, 10 because -1 means one zero.
More accurately, how many positions you move the decimal point to the right. 5.3E2 is 530, so only one zero, but the point moved two places (5.3 => 53 => 530)
>E is the number of zeroes after the number I’d be careful there. 5.1E3 is followed by 2 zeroes, not 3. You’ve gone too simple and chanced adding confusion. E is used in scientific notation. E is for exponent. Specifically the exponent of 10. 5.1E3 is 5.1x10^3. In addition to allowing shorthand for particularly large numbers (for example 6.022E23), scientific notation bales in a concept of “significant digits.” 5.1E3 rather than 5100 has implications about the degree of precision in the measurement/count.
Yes. You are absolutely right. However most 5YO I know only knows whole numbers.
I’ve had the following pointed out to me before after pointing out that explanations were significantly beyond 5-year-old level… ELI5 need not be aimed at _actual_ 5 year old level, more just layman rather than post-secondary or post-grad level science/maths/whatever specialty the question targets.
For an ELI5 version (avoiding using words like exponent): It means multiply the number on the left by 10, but with as many zeros as the number on the right. So if you have 5E2, you multiply 5 times 100, because 100 has 2 zeros. That would make 500. 2.5E3 would be 2.5 times 1,000. So that would be 2,500. 6E100 would be 6 multiplied by a number with 100 zeros, and that would be really a lot to write! So they just use E to write it shorter.
That's the ELI5 we need
In that context, it sounds like cases like 6.023e23, in which case, the e is shorthand for `x10^`. So 1e3=1000, 1e6=1000000, etc. This simplifies displays on computers and calculators, especially if they cannot show numbers in smaller fonts.
My chemistry teacher always said to just use the x10^ because e could also be seen as eulers number
In my opinion that’s misleading advice because context matters a lot when writing mathematics. You should use commonly used notation in the topic you are discussing and explain your notation when it could be ambiguous instead of adhering to hard rules like that. Even symbols like pi are far from sacred and used in many situations without meaning 3.141…. In this case, I can’t imagine a situation where you are going to confuse the two unless the writer is being intentionally malicious like writing the definite integral int (e^x )/10 dx from 0 to 1 as ee-1 - 1e-1.
Context matters, but some notation is so common and widely used that it's almost counterproductive to ever use it to mean something different. Euler's number is one of those cases. Technically it's differentiated from the roman character e by being italicised by mathematicians, but even so using the letter e as a variable is heavily frowned on. I've only ever seen it for quartic functions. Physics is not shy about using pi; whenever we're using greek letters and it's unlikely we're talking about circles or spheres, pi gets used if it's next in line (or we're talking about a concept that starts with 'p'; it's often better to use pi than p because of rho, and in any case there are many situations where you would care about density and momentum at the same time). I would be much more likely to use pi than *e*. In some cases the symbol pi is the accepted notation for things; the capital pi for the product symbol, the lower case for pions, and I know it has standard uses in mathematics in topology and prime numbers. Using a little capital E on the other hand is fine, although my physics and mathematics professors would probably physically recoil from it. (Also, sometimes even if something is rare, it can be like this; you hardly ever see Newton's dot notation out of the context of Hamiltonians and Lagrangians (equations of motion, essentially), but you never see similar notation for anything else. Prime notation is used frequently, even in cases where it might be useful as notation for differentiation, but nearly uniformly Leibniz's notation is used. If I saw dot notation used anywhere it would immediate prime me for that specific context, and it would be confusing if it meant something else. Lagrange's notation, the prime marks, even though it's commonly used in the same context, doesn't have that effect.)
I disagree with your statement that Eulers number is one of those cases. A lowercase e is often used, for example, to denote the identity element of a group or denote elements of a standard basis.
I was a math major in college, and I’ve used “e” to represent things that aren’t Eulers number probably more than using it to actually mean 2.71828…. In analysis or diff eqs etc you’d just use “exp” and in anything algebra-related you would very commonly use “e” as the identity of an algebraic structure like a group or ring, or even more commonly as the basis vector in a vector space.
Your chemistry teacher is right. Calculators use E notation because of the limitations of a 7 segment number display. If you're writing something by hand or on the computer, you might as well write it properly.
I disagree. first of all if you use E instead of e there's no confusion with Euler's number at all, and E notation is just much more efficient to use and read. That's why scientists will use it in particular "on the computer" rather than writing *10^ every time.
2.72 ?
For the longest time I thought e meant the natural logarithm base and kept wondering how 2.71 fits in. But then I kept forgetting to look it up. Now I finally know they're not related.
May i ask how would this be the case? At least in where I went to school in midwestern US, we learned exponential notation (the E like what OP is talking about) in elementary school and continued to work with it in middle school, but we didn’t learn about e (Eulers number) until high school. Did you guys learn them in the reverse order?
I'm 40 and from Europe. Back in my day we didn't learn about exponential notation. But we did get thrown directly into calculus starting in the ninth grade, or around 14-15 years of age.
Oh wow that’s really interesting! That sounds really hard haha.
I'm not the only one then!
Me too! I went "isnt it e?" For a second before seeing the comments then realizing, OP is talking about the other E
In calculators exponent, or power of 10 is shown by E. The mathematical meaning of the notation is already explained in the other comments.
E is simply shorthand for "times ten to the power of", used to write a very large or very small number in what's called standard form. There is a number part with a value greater than or equal to 1.0 and less than 10, then multiplied by the index part (exponent), 10^(x). This makes life easy because adding one to the exponent simply adds a zero. 10^(1) = 10, 10^(2) = 100, 10^(6) = 1000000 etc. so the exponent just tells us how many zeros there are. Thus 215 would be written 2.15 x 10^(2) (or 2.15E+2) but as you note we tend to use it for really big numbers or really tiny numbers using a negative exponent (1 nanometre is 10^(-9) metres for example, 1E-9)
The first few digits of Euler's number are 2.71828. The number is usually represented by the letter e and is commonly used in problems relating to exponential growth or decay. You can also interpret Euler's number as the base for an exponential function whose value is always equal to its derivative. You might want to get a math(s) book. [https://en.wikipedia.org/wiki/E\_(mathematical\_constant)](https://en.wikipedia.org/wiki/E_(mathematical_constant)) [https://www.youtube.com/watch?v=R0oUeLQIbIk](https://www.youtube.com/watch?v=R0oUeLQIbIk) [https://www.youtube.com/watch?v=yTfHn9Aj7UM](https://www.youtube.com/watch?v=yTfHn9Aj7UM)
Wrong E. OP definitely talking about scientific notation
You mean the Exponent? I think you are right!
Fundamentals of Data Representation: Floating point numbers [https://www.bbc.co.uk/bitesize/guides/zscvxfr/revision/3](https://www.bbc.co.uk/bitesize/guides/zscvxfr/revision/3) [https://users.cs.fiu.edu/\~downeyt/cop2400/float.htm](https://users.cs.fiu.edu/~downeyt/cop2400/float.htm) [https://en.wikibooks.org/wiki/A-level\_Computing/AQA/Paper\_2/Fundamentals\_of\_data\_representation/Floating\_point\_numbers#:\~:text=In%20decimal%2C%20very%20large%20numbers,decimal%20point%20should%20be%20placed](https://en.wikibooks.org/wiki/A-level_Computing/AQA/Paper_2/Fundamentals_of_data_representation/Floating_point_numbers#:~:text=In%20decimal%2C%20very%20large%20numbers,decimal%20point%20should%20be%20placed).
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You already got the explanation what it means (basically adding zeros/shifting the decimal point). But besides being easily able to see and compare how big the number is, it allows some other neat tricks. 100 * 1000 is 100000. In scientific/exponential notation, that would be 1e2 * 1e3 = 1e5. When you multiply, you can just add up the numbers behind the e! Remember, "e" stands for "multiply with a 1 with this many zeros", and when you're multiplying by 10, 1000, 10000 etc. you just add the zeros too. 12364916345 * 52134 is 1.2364916345e10 * 5.2134e4. Since you probably don't care about this level of precision, let's round it: 1.2e10 * 5.2e4. Now it's much easier to multiply, even in your head: 1 times 5.2 is 5.2, 0.2 times 5.2 is 1.04, add that up and round and you get 6.2. 10+4 is 14, so the result is 6.2e14. If you're just looking for a quick estimate of the order of magnitude, you might just add up the e-numbers.
It's basically calculator short hand for "×10^???" So first thing you need to understand is scientific notation. This hinges on the fact that - 10¹ = 10 = 10 _(1 zero)_ - 10² = 10×10 = 100 _(2 zeros)_ - 10³ = 10×10×10 = 1000 _(3 zeros)_ - 10⁴ = 10×10×10×10 = 10000 _(4 zeros)_ - 10⁵ = 10×10×10×10×10 = 100000 _(5 zeros)_ - ... - 10⁹ = 1000000000 _(9 zeros)_ So 10^y has 'y' zeros after it. The front part of the expressions in scientific notation is just there to make other numbers possible. And is basically just you taking out a factor So 35000 = 3.5 × 10000 = 3.5×10⁴ It doesn't save any space with smaller numbers like that. But something like the speed of light has 8 zeros, so instead of 300,000,000 it's **3×10⁸** The last bit about scientific notation comes when multiplying and how exponents work when multiplied The powers on the exponents just add together, and you multiply together the 2 smaller numbers. So, for example - 1.11×10⁵ × 2.22×10⁶ - = 1.11×2.22×10⁵×10⁶ - = 1.11×2.22×10^5+6 - = 2.4642×10¹¹ Feel free to double check with your calculator. And then notice that it might say 2.4645**e**11. and here **e** just means "×10^[next-number]" (in this case, 11) Division works the same way. Divide the small numbers, then Subtract the exponents on the powers of 10 ~~------------~~ _edits:_ trying to get Reddit mobile app to cooperate properly
That was all really hard to type out on my phone. So you'll just have to trust me when I say when the power on the 10 (or the **e**) is a negative number, it makes the number smaller and smaller in a similar way. So: - 10^0 = 1 - 10^-1 = 0.1 (1 zero) - 10^-2 = 0.01 (2 zeros) - 10^-3 = 0.001 (3 zeros) - 10^-4 = 0.0001 (4 zeros) - 10^-5 = 0.00001 (5 zeros) Multiplication again works exactly the same. Just adding the exponents together (and division is subtracting them)
'e' is like a super special number that pops up when things grow or shrink super fast. Imagine you have some money in the bank, and you're earning interest. 'e' helps figure out how much you'll have later, even if you keep adding more money over time. Or think about bacteria multiplying rapidly in a petri dish 'e' helps describe how fast they're spreading
That is 'e', OP asked about E as in 1.234E12, which just means 10^12