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