# Range

• Mar 6th 2011, 10:45 AM
Range
can somebody explain this .i don't understand the way used by Matt sir
http://www.sosmath.com/CBB/viewtopic.php?p=214676&highlight=#214676

• Mar 6th 2011, 01:12 PM
emakarov
Let $f(x)=\lfloor x^2\rfloor-\lfloor x\rfloor^2$. Then $\mathop{\mbox{range}}(f)\subseteq\mathbb{Z}$. To prove the converse inclusion ( $\mathbb{Z}\subseteq\mathop{\mbox{range}}(f)$), one must show that every integer $n$ is in the range of $f$. For this, one needs to find a pre-image of every integer. Matt showed that $f(n+1/2)=n$.
• Mar 6th 2011, 05:25 PM