Justification of a floor function simplification

Question

Consider the expression: $\left\lfloor\frac{k+1}{2}\right\rfloor$, Where $k \in \mathbb{N}$ (natural numbers)

How would I show that $\left\lfloor\frac{k+1}{2}\right\rfloor$ is the same thing as $\left\lfloor\frac{k}{2}\right\rfloor$ .

Answer 1

This is not true $$ \left\lfloor \frac{k+1}{2} \right\rfloor = \left\lfloor \frac{k}{2}+\frac{1}{2} \right\rfloor $$ In the case that $k=3$, $$ \left\lfloor \frac{3}{2}+\frac{1}{2} \right\rfloor = \left\lfloor 2 \right\rfloor \ne \left\lfloor 1.5 \right\rfloor $$