Questions tagged [ceiling-and-floor-functions]

This tag is for questions involving the greatest integer function (or the floor function) and the least integer function (or the ceiling function).

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How can one find the x value that gives the largest possible value to the equation (100floor(10000/(floor(100000/(2x))+1)))/x?

How can one find the x value that gives the largest possible value to the equation $$\frac{100\left\lfloor\frac{10000}{\left\lfloor \frac{100000}{2x}\right\rfloor+1}\right\rfloor}{x}$$ where $x$ is a ...
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Continuity of composition of root and floor function

Can someone give me a hint to prove the continuity of the following function: $f: \mathbf{R}\to\mathbf{R}, f(x):=\sqrt{\lfloor{x^2}\rfloor}$. I already proved the continuity of the root function and ...
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Proving $\left\lfloor \sqrt{x^2+3x+3}\right\rfloor = x+1$
Let $$f(x)=\sqrt{x^2+3x+3}$$ Claim: $$\lfloor f(x)\rfloor = x+1$$ I came across this expression in a question and made this claim based on observations $$⌊f(1)⌋=\lfloor\sqrt{7}\rfloor=2$$ ⌊f(2)⌋=\...