Where does the irrational e come from (2.71828 ... ) and why is it so important?

Answer 1

It is the base of "natural" logarithms (represented by "ln x"), which are defined by: ln x = integral from 1 to x of 1/x dx. Thus it's defined by ln e = 1. It can also be defined in other ways. See this web page for all of the details: http://mathworld.wolfram.com/e.html.

Answer 2

e is defined in many ways

lim x -> 0 ( 1 + x ) ^ ( 1 / x )
lim x -> infty ( 1 + 1/x ) ^ x

sum_i=0 ^ infty 1/ i!

The number such that; ln (e) = 1

It is so important because it is a number that shows up so much in mathematics (and anything that uses mathematics)

The famous numbers are e, pi, i as they are always around in mathematics

See the source for more 'exciting' information

Answer 3

e = 2.718281828...... is an irrational number. There are many expressions that result in e.

e = lim (x -> 0) (1 + x)^(1/x)
e = lim (x-> ∞) (1 + 1/x)^x
e = ∑ (i = 0 -> ∞) 1/i!

It is also the number such that
d/dx (e^x) = e^x
ln e = 1

^_^

Answer 4

like pi, e turns out to be one of the arbitrary universal constants. there are only about 30 or so of these 'constants' defined so far to date. like the charge on a single electron, so far it simply 'is' because it isn't anything else.

Answer 5

e is known as euler's number, it equals (1+t)^1/t
It's important in natural logarithms

Answer 6

It describes natural functions and interest.

http://en.wikipedia.org/wiki/E_constant

Answer 7

If I remember right, it is used for continuously compounded interest.