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Integrating Floor Functions $\int_0^{1102} \lfloor{x^{1/2}}\rfloor \mathrm{d}x$

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#calculus #integration #ceiling-and-floor-functions
162
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Prove that $⌊xy⌋ \le ⌊x⌋⌊y⌋ + ⌊x⌋+⌊y⌋$ for $x,y \in \mathbb{R}$, as $x,y>0$

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#number-theory #ceiling-and-floor-functions
988
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$\lfloor x^n\rfloor\lfloor y^n\rfloor$ is a perfect square

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#number-theory #elementary-number-theory #ceiling-and-floor-functions #square-numbers #perfect-powers
54
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Evaluation of integrals with floor functions

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#definite-integrals #ceiling-and-floor-functions
413
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How to simplify an equation with a floor function

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#ceiling-and-floor-functions
166
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Evaluating limits of floor functions

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#limits #ceiling-and-floor-functions
432
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$\lim_{x\to6^-}\big[\frac{\sqrt{36-x^2}}{x-6}\big]$ using L'Hopital's rule?

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#calculus #limits #derivatives #radicals #ceiling-and-floor-functions
48
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Need help writing a recursive formula for the following sequence

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#sequences-and-series #discrete-mathematics #recurrence-relations #ceiling-and-floor-functions
97
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prove that $(n!)^{(n-1)!}$ divides (n!)!

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#number-theory #elementary-number-theory #prime-numbers #factorial #ceiling-and-floor-functions
119
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$20\{x\} = x + [x] + [x + 0.5]$

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#elementary-number-theory #contest-math #ceiling-and-floor-functions
49
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Limit doesn't turn out as expected

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#limits #trigonometry #ceiling-and-floor-functions
191
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What does $\sum \mu(d)\lfloor{\frac{x}{d}}\rfloor$ count?

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#number-theory #analytic-number-theory #ceiling-and-floor-functions #mobius-function #mobius-inversion
49
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Prove $2^{\lceil \lg (n-1) \rceil} \ge n-1$

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#algorithms #ceiling-and-floor-functions
305
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Greatest Integer Function/Floor Function Definition? (Discrete Mathematics)

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#discrete-mathematics #ceiling-and-floor-functions
212
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Proving surjectivity of a floor function.

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#functions #discrete-mathematics #elementary-set-theory #ceiling-and-floor-functions

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