Floor Function/Examples/Floor of 5 over 2

From ProofWiki
Jump to navigation Jump to search

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.

$\blacksquare$


Sources