Proof that e is irrational Guide, Meaning , Facts, Information and Description
In
mathematics, the series expansion
-
of the number
e can be used to prove that
e is
irrational.
Suppose e = a/b, for some positive integers a and b. Consider the number
We will show that
x is a positive integer less than 1, and this contradiction will establish the irrationality of
e.
- To see that x is an integer, note that
Here, the last term in the final sum is to be interpreted as an empty product.
- To see that x is a positive number less than 1, note that
Here, the last sum is a geometric series.
Since there does not exist a positive integer less than 1, we have reached a contradiction, and so
e must be irrational. This completes the proof.
Q.E.D
This is an Article on Proof that e is irrational. Page Contains Information, Facts Details or Explanation Guide About Proof that e is irrational
