Proof That E Is IrrationalYou are currentlybrowsing as guest. Click here to log in 

The number e also known as Euler's Number, is irrational. This page could be replaced by a reference to a good proof elsewhere.
The number e can be defined as:
Now we multiply both sides by b!
Hence $\frac{1}{(b+1)}+\frac{1}{(b+1)(b+2)}+\frac{1}{(b+1)(b+2)(b+3)}+...$ is strictly between 0 and 1.
This contradicts the requirement that expression (*) must be an integer.
Thus we cannot have $e=a/b$ and so e is not a rational number  It's an irrational number.
Last change to this page Full Page history Links to this page 
Edit this page (with sufficient authority) Change password 
Recent changes All pages Search 