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Math Help - Direct Proof

  1. #1
    Junior Member mant1s's Avatar
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    Direct Proof

    Hi Community,

    I am having some trouble with this question:

    "Show that the additive inverse, or negative, of an even number is an even number using a direct proof. "

    I know it's basically asking me to prove that the inverse of an even number is even. I'm having trouble expressing it in English/ Mathematical operators.

    I have:

    Let n = 2a, for all !n=2a, n is even

    Someone help?

    -M
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  2. #2
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    The additive inverse of a number x is denoted -(x)

    All even numbers are defined to be \{ 2a | a\in\mathbb{Z} \}

    So we have an even number. Let's call it 2a.

    Well it's inverse is -(2a)=(-1)(2a)=(2a)(-1)=2(a(-1))=2(-a), but if a\in\mathbb{Z}, then -a\in\mathbb{Z}, and so -(2a) is an even number
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