Sunday, 26 May 2013

மூளைக்கு வேலை - 18

Is zero odd or even?





Zero is even, under three separate but related analyses.

Number Line - consecutive integers vary by 1, and each successive integer changes parity, from odd to even or even to odd.


Additive rules - even + even = even, odd + odd = even. Under this rule, zero can be even but cannot be odd.


The definition of an even number - divisible by 2 with no remainder.


The most commonly accepted definition is that the number "a" is even if there exists an integer "n" which makes the following statement true:

a = 2 x n

0 is an integer. So let n = 0 in the above equation and we get

0 = 2 x 0


So 0 satisfies the mathematical definition for being even.

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