Prove that if æ is a positive real number, then LV=]] = LVE] %3D

Solution:

Definition:

The Floor function $f$ is a function that takes any real number $x$ and gives $f\left(x\right)$, a real number which is the greatest integer less than or equal to x.

The function $f$ is denoted by, $f\left(x\right)=⌊x⌋ \forall x\in \mathrm{ℝ}$.

Example:

1> If $n\in \mathrm{\mathbb{Z}}$, then $f\left(n\right)=n \forall n\in \mathrm{\mathbb{Z}}$.

2> If $a\in \mathrm{ℝ}$ be any real, then $\exists$an unique integer $n$ with $n<a<n+1$. Then $⌊a⌋=n$.