- #1
iamalexalright
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Homework Statement
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]
Homework Equations
The field axioms(closure, associativity,...)
The order axioms
Definition of the absolute value (and a few theorems)
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?)