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 $a,b \geqslant 0$. If $a \leqslant M_1$, $b \leqslant M_2$ for some $M_1, M_2 >0$, then how can I find $c$ such that $$ |a-b| \leqslant c|M_1 - M_2 | ?$$

share|improve this question
    
Think about M1-a , M2-b. They are both greater than 0 –  Adam Rubinson Nov 7 '12 at 10:56

1 Answer 1

up vote 2 down vote accepted

Take $a = 2$, $b = 1$ and $M_1 = M_2 = 3$. For any $c$, we have $$ \lvert a - b \rvert = 1 > c\lvert M_1 - M_2\rvert = 0 $$ Hence, a number $c$ satisfying the proposed inequality does not need to exist.

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.