MHB Graph Function: What Does It Mean?

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What does the function even mean?
 

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That is one way to denote the floor function, more commonly given as $$\lfloor x \rfloor$$, which means the largest integer not greater than $x$. Its value at $x$ is called the integral part or integer part of $x$. The fllor function may be defined by the set equation:

$$\lfloor x \rfloor=\max\{m\in\mathbb{Z}\,|\,m\le x\}$$
 

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