Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Let $f(x)$ and $g(x)$ be functions. I'm looking for an upper bound on $-\min(-f(x), -g(x))$, but the minus signs are making me dizzy. Is this the same as an upper bound on $\max(f(x),g(x))$?

share|improve this question
2  
Is this easier to see: $\min(-a,-b)=-\max(a,b)$? –  Srivatsan Sep 23 '11 at 14:24

1 Answer 1

up vote 2 down vote accepted

Pick a number $K$.
$$ -\operatorname{min}(-f,-g) \leq K \iff \operatorname{min}(-f,-g) \geq -K $$ Using Srivatsan's suggestion, this is $$ -\operatorname{max}(f,g) \geq -K $$ which is equivalent to $\operatorname{max}(f,g) \leq K$. So you were right!

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.