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

Let F and G be bounded functions on S. If f(x) <= g(x) for all x in S prove that inf{f(x):x belongs to S} <= inf{g(x):x belongs to S}

2. Relevant equations

None

3. The attempt at a solution

Basically the idea is to let L_{0}= inf{f(x):x belongs to S} and L_{1}= inf{g(x):x belongs to S} and show that L_{0}<=L_{1}

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# Inequality proof involving Infs and Sups

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