0 and 1
The numbers 0 and 1 play an important role in mathematics.
Example 1
The series for the exponential function is
If you write it in much detail you get
For x = 0 it becomes
Because e = 2.7182… this gives e0 = 1. The series can therefor be written as
There are infinitely many terms, but they are all 0, exept for one. That first term must then be 1. The numerator and the denominator are thus equal, so
That should be, as by definition 00 ≝ 1 and 0! ≝ 1.