Question

Where does e come from? I need a good explanation, I know that it's its own derivative, the limit as n approaches infinity of (1+1/n)^n but that doesn't tell me much about what that means.

Answer 1

@inkyvoyd explain him in a simpler way!! u r good in that!

Answer 2

Well

Answer 3

There was this one dude named Bernoulli.

Answer 4

From a large family of people named Bernoulli.

Answer 5

This guy was experimenting with something.

Answer 6

Wikipedia explains well.
"An account starts with $1.00 and pays 100 percent interest per year. If the interest is credited once, at the end of the year, the value of the account at year-end will be $2.00. What happens if the interest is computed and credited more frequently during the year?"

Answer 7

Let's say, every 6 months it is computed.

Answer 8

then, after the first 6 months, you get 1.5 dollars (50% interest twice), and after the second 6 months, you get 1.5*1.5=2.25

Answer 9

What if interest is compounded every 3 months?

Answer 10

then, we have 1.00$*1.25*1.25*1.25*1.25

Answer 11

or, 1*1.25^4

Answer 12

or, simply 1.25^4

Answer 13

Now, the question is, what happens when we try to take the interest rate daily, every minute, every second, every (shorter period of time)? Now how bout time ->0?

Answer 14

We get (1+1/n)^n as n-> infinity, or e.

Answer 15

@Kainui , the significance of this was that Bernoulli here tried to compute this limit, and found it very difficult.

Answer 16

There are many other uses of e, and many places it turns up. Ican give you some examples.

Answer 17

Ever heard of e^(ipi)+1=0?

Answer 18

Useful equation in complex analysis.

Answer 19

god gave it to us:) this is the only thing I can come up with, and I dont believe in god

Answer 20

If you understand derivatives of trig functions, I can prove it.

Answer 21

and, btw, your question is the equivalent to "where does pi come from?"

Answer 22

Sure, you might answer with "a circle"

Answer 23

the oven

Answer 24

but one could answer the question about e similarly, with "exponential growth"

Answer 25

trolol, @zzr0ck3r

Answer 26

e is much cooler than pi imo

Answer 27

i is much cooler than both imo.

Answer 28

No pun intended.

Answer 29

i is not real

Answer 30

@Kainui who went offline, hopefully you understand.

Answer 31

You aren't?

Answer 32

:)

Answer 33

you cant really think i is cooler than e?

Answer 34

i *am* cooler than e.

Answer 35

how do i unfan someone...jk

Answer 36

and really, i and e are so related I can't think one is cooler than the other

Answer 37

im in dif eq right now so e rules my life:)

Answer 38

Well, I'll be in complex analysis in like 5 years, and they will both rule my life.

Answer 39

Not that they don't.

Answer 40

5 years? what are you in now?

Answer 41

Well, I haven't *formally* taken trig.

Answer 42

:S

Answer 43

lol, good for you.

Answer 44

not sarcastic ^

Answer 45

Differential equations sound really cool though

Answer 46

skimmed pauls notes on first order linear ODE solution

Answer 47

felt like the cubic man

Answer 48

its great until you notice most dif eqs have no solutions, so its lots of numeric and qualative stuff...boring i want answers

Answer 49

Well, all an engineer wants is numbers right?

Answer 50

But, do you mean, no solutions, or no ways to solve?

Answer 51

no *known ways

Answer 52

nah there are existence theorems

Answer 53

A lot of it is doing numerical approximations of solvable ones, right?

Answer 54

not that I know of, most of them are unsolvable

Answer 55

we can get lots of information about the solution, but we cant find it

Answer 56

the general solution that is

Answer 57

is it proved that we can't solve it, or that we just don't know how to?

Answer 58

Is it the quintic without Bring radicals, or the quartic before the cubic is solved?

Answer 59

I just asked the same question today, so there are some we can show that there are no solutions because of proofs that the integral is unsolvable, so im guessing the answer is out there but we dont know how to find it. In other words there is still cool stuff to figure out:)

Answer 60

Exactly.

Answer 61

You know how long it took us to solve the cubic?

Answer 62

600 years ish?

Answer 63

Let's just say we didn't actually "solve it" (casus irreduciblis) until hypergeometric series.

Answer 64

Also, Euclid, eat that, you can't take the cube root of 2, sucker :D

Answer 65

haha

Answer 66

shh they might burn you

Answer 67

lol

Answer 68

They had enough trouble understanding the square root of two.

Answer 69

such an easy proof for that one also, so crazy...

Answer 70

apparently negative numbers were less accepted than irrational positve ones

Answer 71

Stupid geometry

Answer 72

Screwed us over for centuries man

Answer 73

then again it took galileo to roll a marble down a tilt .....

Answer 74

looool

Answer 75

they need to make a movie about math history, people have no idea

Answer 76

There's plenty, just no one wuld ever watch a math documentary about math history

Answer 77

im thinking somehitng like the dan brown books, not a docu. A big movie with all the cool math history and then people would get into it

Answer 78

Dan brown would make a terrible movie about math. He doesn't believe in imaginary numbers

Answer 79

Napier, logarithms.....

Answer 80

of course, why didn't I see it before?