# Concept derivation guides

299 concept teaching guides, separate from the 36,000 individual question derivations.

[Search all questions & derivations →](/en/explore/)

1 1 results · Page 1 of 1



Concept guide



## [Absolute value: nonnegativity, the zero case and |a−b|=|b−a| from the piecewise definition](/en/derivations/derivation-mko-absolute-value-01/?from=%2Fen%2Fderivations%2F%3Fq%3Dmko-absolute-value)

Using only the piecewise definition (|x|=x when x≥0, |x|=−x when x<0) together with the order and addition of the reals, prove for all reals x, a, b: (1) |x|≥0; (2) |x|=0 ⇔ x=0; (3) |−x|=|x|; (4) |a−b|=|b−a|. Then compute |−3|, |2−7| and |7−2|, and show that '|x|=x for every x' is false.

Absolute value

derivation-mko-absolute-value-01





1 1 results · Page 1 of 1