# Concept derivation guides

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Concept guide



## [The usual order on ℝ: translation, cross-multiplication with positive denominators, finite extrema and closed intervals](/en/derivations/derivation-mko-order-relation-01/?from=%2Fen%2Fderivations%2F%3Fq%3Dmko-order-relation)

Prove for all reals a, b, c that a<b ⇔ a+c<b+c; that p/q<r/s ⇔ ps<rq when q, s>0; and that a finite nonempty set of reals has a minimum, which is unique. Use these to compare the elements of M={−5/9, 1/3, −7/12, −1/2} (listed in this order), find the minimum and maximum of M, and decide whether the two endpoints and 1/2 belong to the closed interval [min M, max M].

Usual order on the real numbers

derivation-mko-order-relation-01





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