[Home]Irrational number

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An irrational number is any real number that is not a rational number, i.e., it cannot be written as a fraction a / b with a and b integers and b not zero.

Examples of irrational numbers are 21/2 (the square root of 2) and 31/3 (the cubic root of 3).

The first proof of the irrationality of 21/2 is usually ascribed to Pythagoras or one of his followers and seen as the discovery of the irrational numbers. This proof proceeds as follows.

This proof is an example of Reductio ad absurdum.

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Last edited July 20, 2001 5:32 am by 212.83.74.xxx (diff)