Infinity

Infinity is not an actual number but something which is approached as a limit. For instance, the operation of division by zero is undefined, but the function <math>F</math>_x = <math>1/x</math> approaches infinity as x approaches zero.

Georg Cantor's diagonal argument is an elegant proof demonstrating that the infinity of real numbers is greater than the infinity of countable integers. The essence of the argument is that in any proposed list of all real numbers, a new real number not in the list can be constructed by taking the digits in a diagonal through the list and changing them to construct a new real number that differs from the nth entry at the nth position right of the decimal point.

Infinity is written using the symbol ∞

However, in some non-standard model of Peano arithematic, ∞ is treated as an actual number.