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I have two prepositions to prove with the basic axioms for addition and multiplication:

  1. For all $m \in\mathbb Z$, $-(-m) = m$

\begin{align*} (-m) + -(-m) &= 0\\ (-m) + m &= 0 \\ (-m) + -(-m) &= (-m) + m \\ m + (-m) + -(-m) &= m + (-m) + m\\ 0 + -(-m) &= 0 + m \\ -(-m) &= m \end{align*}

  1. $-0 = 0$

\begin{align*} (-0) + -(-0) &= 0\\ (-0) + 0 &= 0\\ (-0) = 0\\ \end{align*}

The second step is based on the first preposition.

I would greatly appreciate the community's feedback. Thank you!

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    $\begingroup$ You did well! It's totally correct. $\endgroup$
    – Henry
    Commented Feb 7, 2015 at 1:28
  • $\begingroup$ @Spark Alright! :D thank you! $\endgroup$
    – Johnathan
    Commented Feb 7, 2015 at 1:28

1 Answer 1

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Your proofs are sufficiently correct.

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