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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 - \(even + even = even\) and \(odd + odd = even\). 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: \(a = 2 \times n\). Since\(0\) is an integer, so let \(n = 0\) in the above equation and we get \(0 = 2 \times 0\).

So \(0\) satisfies the mathematical definition for being even. Akshat Jain · 4 years, 1 month ago

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I feel that if the definition of an odd number is an integer of the form 2k+1, then 0 must be an even number, and should not be an odd number. Siddharth Kumar · 4 years, 1 month ago

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