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$\begingroup$

$f:R \rightarrow R$

$f(x)$ = $(-1)^x$ $\lfloor(1+x)/2\rfloor$

So how do you prove it when you have a floor function?

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    Hi, welcome here.Are you sure your function is $\mathbb R \to \mathbb R$ ? As putting $x= -\frac 12$ contradicts this??2012-11-09
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    Matthew: I'd suggest changing the first $R$ to $N$ and the second $R$ to $Z$, and maybe use $n$ instead of $x$ for the variable (most math folks think of $x$ as representing a real number, and if they see $n$ will assume it's a natural number).2012-11-09

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