MHB Graph Function: What Does It Mean?

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The floor function, denoted as $$\lfloor x \rfloor$$, represents the largest integer that is not greater than a given value $x$. This function is also referred to as the integral part or integer part of $x$. It can be formally defined using a set equation that identifies the maximum integer $m$ such that $m$ is less than or equal to $x$. Understanding the floor function is essential in various mathematical applications, particularly in discrete mathematics and computer science. The floor function plays a crucial role in rounding down real numbers to their nearest integers.
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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:

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

Thread 'Trigonometry problem of interest'

Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
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