Floor Function/Examples/Floor of 5 over 2

Theorem

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

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

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.

$\blacksquare$