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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 $$ |a-b| \leqslant c|M_1 - M_2 | ?$$

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

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