(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The positive part of an a in R is defined by:

[tex]a^{+} = (|a| + a) / 2[/tex]

and the negative by:

[tex]a^{-} = (|a| - a) / 2[/tex].

Prove that [tex]a = a^{+} - a^{-}[/tex] and [tex]|a| = a^{+} + a^{-}[/tex]

2. Relevant equations

The field axioms(closure, associativity,...)

The order axioms

Definition of the absolute value (and a few theorems)

3. The attempt at a solution

Now, I'm new at proof writing, but this seems too simple (and I don't know if providing all these steps is too much or not?) : /

[tex]a = a^{+} - a^{-}

= (|a| + a)/2 - (|a| - a)/2

= 2^{-1}(|a| + a) - 2^{-1}(|a| - a)

= 2^{-1}(|a| + a - |a| + a)

= 2^{-1}(2a)

= a

[/tex]

(btw, how can I separate my proof line by line with LaTeX?)

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# Homework Help: Easy Analysis Proof

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