Discrete Mathematics functions Prove that if $n$ is an integer,then > $[n/2]=n/2$ if $n$ is even > > $[n/2]=(n-1)/2$ if $n$ is odd I want to know the methodical answer for this question, I have reached out here to the same question unfortunately he hasn't added the full answer.

The function $\;\lfloor x\rfloor\;$ is "the integer part of $\;x\,$" or "floor function", which means: the greatest integer number _which is still less than or equal_ $\;x\;$ . So if $\;n=2k\;,\;\;k\in\Bbb Z\;$ is even , then

$$\left\lfloor\frac n2\right\rfloor=\lfloor k\rfloor=k=\frac{2k}2=\frac n2$$

Now you try to figure out the other one, taking into account that if $\;n\;$ is odd, then $\;n=2k+1\;$ .