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formal definition of limit to prove floor function limit

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A question about the function $S(n)=\sum_{p\le\sqrt n}\Big\lfloor\frac n p\Big\rfloor$

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Related to Discontinuity Property of Floor Function

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Range of error in truncated division $\lfloor\frac{a\pm 1}{b\pm 1}\rfloor$

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How to solve inequality equation with ceil operator product

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Limit of $\lim_{x\to\infty}\frac{\int_0^xt-\lfloor t\rfloor dt}{x}$

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List Question

How to solve a quadratic equation with floor function

A Number theoretic inequality including floor functions.

USAMO problem solution using APMO problem.

Solving an equation that involves both ROUND and ROUND-DOWN

Is there an easy way to compare floors and ceilings? Eg, is it true that $\lfloor{\frac{n}{k}}\rfloor\leq\lceil{\frac{n+1}2}\rceil$ for $k\geq 2$?

How to solve $ \lfloor x+2\rfloor-1=0 $

How to plot and analyze function $f(x)=x+\lfloor x \rfloor+\operatorname{Sgn}(x)+1$

formal definition of limit to prove floor function limit

Diophantine equation in two variables involving floor function

How to solve $\left\lfloor y_1 2^z\right\rfloor -\left\lfloor y_2 2^z\right\rfloor =x$ for $z$ in terms of $y_1,y_2$ and $x$?

A question about the function $S(n)=\sum_{p\le\sqrt n}\Big\lfloor\frac n p\Big\rfloor$

Related to Discontinuity Property of Floor Function

Range of error in truncated division $\lfloor\frac{a\pm 1}{b\pm 1}\rfloor$

How to solve inequality equation with ceil operator product

Limit of $\lim_{x\to\infty}\frac{\int_0^xt-\lfloor t\rfloor dt}{x}$

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