Formula for the floor of $n/2$, to be proved by induction

Question

How do you compute this when the base case is all wrong?

Answer 1

HINT:

Use $$\left\lfloor\frac{m+2}2\right\rfloor=\left\lfloor\frac m2+1\right\rfloor=\left\lfloor\frac m2\right\rfloor+1$$

In fact, $$\left\lfloor\frac mn+I\right\rfloor=\left\lfloor\frac mn\right\rfloor+I$$ for any integers $I,m,n$