Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I'm actually doing an exercise where I have to draw graphs of functions. I understand r=|s| but not |r|=|s|. Are they the same?

share|cite|improve this question
$r=|s|$ means that $r\geq 0$. Is this true if $|r|=|s|$? – user12477 Sep 18 '12 at 21:25
up vote 3 down vote accepted

They are not the same. If $r=|s|$, then $r$ can never be negative, but $|r|=|s|$ is true if $r=-1$ and $s=1$ (or for that matter if $s=-1$). The statement that $|r|=|s|$ just says that $r=\pm s$, i.e., that $r=s$ or $r=-s$: in both cases $r$ and $s$ will have the same absolute value, regardless of their algebraic signs.

share|cite|improve this answer

Let $r = 4$ and $s = -4$. Then, $r = |s|$ and $|r| = |s|$.

Then, switch it around. Let $r = -4$ and $s = 4$. Then, $|r| = |s|$ but $r \neq |s|$.

So they are not always the same.

share|cite|improve this answer

Your Answer


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.