Diagonal_slash_argument
A logical argument devised by Georg Cantor to demonstrate that the real numbers are not countably infinite.
It proceeds as follows:
Suppose the real numbers are countably infinite.
We may now enumerate them as a sequence, {r1,r2,r3,...}
We shall now construct a real number, x, by considering the nth digit of the decimal expansion of rn. x will be between 0 and 1.
If this nth digit of rn is 0, let the nth in digit the decimal expansion of x be 1
Otherwise, let the nth in digit the decimal expansion of x be 0
x is clearly a real number, but it differs in the nth decimal place from rn, so x is not in our enumeration of the real numbers.
This contradicts our supposition that the reals are countably infinite, and therefore our supposition is false.
