What equation (sequence) would resolve any number into either odd or even?

[Dzuong N]

Hello all,I'm having trouble trying to figure out an equation that will categorize any number to either zero (for even numbers) and one (for odd numbers). For example:0 = 0 (even)1 = 1 (odd)2 = 0 (even)3 = 1 (odd)4 = 0 (even)5 = 1 (odd)6 = 0 (even)7 = 1 (odd)Any help would be much appreciated. Thanks!

[ya_tusik]

Well the typical way is to define a function that has two possible values. i.e.f(x) = 0 (for all x even)f(x) = 1 (for all x odd)This is a perfectly valid function.

[shanikqua g]

well if you take the square root of the even or odd number than the even number will be a whole number or irrational number if you know what i am saying you would know.

[Steiner]

The sequence a_n = (1 - (-1)^n)/2 does the job. Just check

[Stew]

With the exception of zero, X-(X+1) would work. Zero would end up being odd even though it is neither odd nor even.

[knashha]

n is even if and only if (-1)^n = 1 help, or no?