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 $$ |a-b| \leqslant c|M_1 - M_2 | ?$$
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.
Here's how it works:
- Anybody can ask a question
- Anybody can answer
- The best answers are voted up and rise to the top
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.