E

   Euler's number (not to be confused with [1]Euler number), or e, is an
   extremely important and one of the most fundamental [2]numbers in
   [3]mathematics, approximately equal to 2.72, and is almost as famous as
   [4]pi. It appears very often in mathematics and nature, it is the base of
   natural [5]logarithm, its digits after the decimal point go on forever
   without showing a simple pattern (just as those of [6]pi), and it has many
   more interesting properties.

   It can be defined in several ways:

     * Number e is such number for which a [7]function f(x) = e^x (so called
       [8]exponential function) equals its own [9]derivative, i.e. f(x) =
       f'(x).
     * Number e is a [10]limit of the infinite series 1/0! + 1/1! + 1/2! +
       1/3! + ... (! signifies [11]factorial). I.e. adding all these
       infinitely many numbers gives exactly e.
     * Number e is a number greater than 1 for which [12]integral of function
       1/x from 1 to e equals 1.
     * Number e is the base of natural [13]logarithm, i.e. it is such number
       e for which log(e,x) = area under the function's curve from 1 to x.
     * ...

   e to 100 decimal digits is:

   2.7182818284590452353602874713526624977572470936999595749669676277240766303535475945713821785251664274...

   e to 100 binary digits is:

   10.101101111110000101010001011000101000101011101101001010100110101010111111011100010101100010000000100...

   Just as [14]pi, e is a [15]real [16]transcendental number (it is not a
   root of any polynomial equation) which also means it is an [17]irrational
   number (it cannot be expressed as a fraction of integers). It is also not
   known whether e is a [18]normal number, which would means its digits would
   contain all possible finite strings, but it is conjectured to be so.

   TODO

Links:
1. euler_number.md
2. number.md
3. math.md
4. pi.md
5. log.md
6. pi.md
7. function.md
8. exp.md
9. derivative.md
10. limit.md
11. factorial.md
12. integration.md
13. log.md
14. pi.md
15. real.md
16. transcendental.md
17. irrational.md
18. normal_number.md