5
$\begingroup$

For Christmas I got a math watch and for 4 it was $-[-\pi]$. I know that $\pi$ does not equal 4 so how does $-[-\pi]$ equal 4? Thank you.

$\endgroup$
  • 2
    $\begingroup$ The symbol $[ \cdot ]$ means to take the floor. It's not a general bracket. The floor of $-\pi$ is $-4$ (since it is the largest integer smaller than $-\pi$) and then taking the negative of it gives you $4$. $\endgroup$ – Cameron Williams Dec 27 '15 at 2:45
  • $\begingroup$ what do that $[.]$ stand for? $\endgroup$ – mrs Dec 27 '15 at 2:46
  • $\begingroup$ I think the $\cdot$ was meant as a place holder. $\lfloor x \rfloor$ means the largest integer less than or equal to x. $\endgroup$ – fleablood Dec 27 '15 at 3:02
  • $\begingroup$ Sounds like it should have just been $\lceil \pi \rceil$. That's gimmicky enough. $\endgroup$ – Em. Dec 27 '15 at 3:08
  • $\begingroup$ "should"? "gimmicky enough"? the entire point of the watch is to be convoluted so "$-\lfloor \pi \rfloor$ is *much better than ceiling pi because it's much less direct. $\endgroup$ – fleablood Dec 27 '15 at 3:32
6
$\begingroup$

$[x]$ is the floor of $x$, the largest integer less than or equal to $x$. For example $[4.6]=4$, $[7]=7$ and $[-67.4]=-68$.

So $-[-\pi]=-(-4)=4$

$\endgroup$
  • $\begingroup$ @CameronWilliams Thanks :) $\endgroup$ – user223391 Dec 27 '15 at 2:48
  • $\begingroup$ Thank you! So is [x] just called the floor? or is there another name for it? $\endgroup$ – 3141 Dec 27 '15 at 2:52
  • $\begingroup$ Isn't $[x]$ often the nearest integer? $\endgroup$ – TokenToucan Dec 27 '15 at 2:55
  • 2
    $\begingroup$ @ArchisWelankar That wouldn't make sense here. $\endgroup$ – user223391 Dec 27 '15 at 3:33
  • 2
    $\begingroup$ @user236182: Not "the nearest integer to $n$", but rather "$n$ rounded up to the nearest integer". There is no such thing as "the nearest integer" since, for example, $0$ and $1$ are equally near to $\frac12$. $\endgroup$ – MPW Dec 27 '15 at 4:14
1
$\begingroup$

Well... $[ x ]$ gives the largest integer $\leq x$. That is, $[ x ] = \sup\{z : z \in \mathbb{Z}, z\leq x\}$ if one likes to complicate things. Anyway, it's rather straightforward to prove your claim: $$- [ - \pi ] = - [ -3.1415\ldots\, ] = - (-4) = 4$$

$\endgroup$
0
$\begingroup$

Hint: By definition, $x=[x]+\{x\}.$ By convention, $\{x\}\ge0$.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

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