# Floor Function/Examples/Floor of 5 over 2

## Theorem

$\floor {\dfrac 5 2} = 2$

where $\floor x$ denotes the floor of $x$.

## Proof

We have that:

 $\displaystyle \dfrac 5 2$ $=$ $\displaystyle 2 + \dfrac 1 2$ $\displaystyle \leadsto \ \$ $\displaystyle 2$ $\le$ $\displaystyle \dfrac 5 2$ $\displaystyle$ $<$ $\displaystyle 3$

Hence $2$ is the floor of $\dfrac 5 2$ by definition.

$\blacksquare$