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'''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 <br><br><math>F</math>_x = <math>1/x</math> approaches infinity as x approaches zero.

'''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.

[[Georj 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.

[[Georj 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.