Proving Even Number Additive Inverse is Even

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Homework Help Overview

The discussion revolves around proving that the additive inverse of an even number is also an even number, focusing on direct proof methods in the context of basic number theory.

Discussion Character

  • Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster expresses uncertainty about how to approach the proof. One participant suggests defining an even number in terms of its representation, while another hints at a different starting point for the proof.

Discussion Status

The conversation includes attempts to clarify the concept of even numbers and their additive inverses. Some guidance has been provided, but there is no explicit consensus on a single method or approach yet.

Contextual Notes

Participants are working within the constraints of a direct proof requirement and are exploring definitions and properties of even numbers.

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Homework Statement


How do I show that the additive inverse, or negative, of an even number is an even number ( direct proof) ?


Homework Equations





The Attempt at a Solution



I have no idea. Anybody?
 
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Really? Let [tex]a=2n[/tex] be an even number then the additive inverse [tex]b[/tex] is defined by [tex]a+b=0[/tex], so [tex]b=-a=-2n[/tex], and so...
 
alternatively, start "an even number is a + a, so …" :wink:
 
Thanks! Makes sense now.
 

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