Floor Function/Examples/Floor of 3

Theorem

$\floor 3 = 3$

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


Proof

We have that $3$ is an integer.

Thus this is a specific example of Real Number is Integer iff equals Floor:

$\floor x = x \iff x \in \Z$

$\blacksquare$


Sources

  • 1965: J.A. Green: Sets and Groups ... (previous) ... (next): Chapter $2$. Equivalence Relations: Exercises $3$
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