A number n is odd if there is an integer k such that n = 2k + 1. One way to prove that zero is not odd is by contradiction: if 0 = 2k + 1 then k = −1/2, which is not an integer.[15] Since zero is not odd, if an unknown number is proven to be odd, then it cannot be zero. This apparently trivial observation can provide a convenient and revealing proof explaining why a number is nonzero.

A number n is odd if there is an integer k such that n = 2k + 1. One way to prove that zero is not odd is by contradiction: if 0 = 2k + 1 then k = −1/2, which is not an integer.[15] Since zero is not odd, if an unknown number is proven to be odd, then it cannot be zero. This apparently trivial observation can provide a convenient and revealing proof explaining why a number is nonzero.