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Definition of floor in terms of <

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#ceiling-and-floor-functions
101
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Show fractional part of integer multiplied by irrational is not equal to different integer multiplied by same irrational.

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#real-analysis #analysis #ceiling-and-floor-functions
748
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Proving $m!(n!)^m \mid (mn)!$ and $m!n!(m+n)! \mid (2m)!(2n)!$ algebrically

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#combinatorics #elementary-number-theory #prime-numbers #ceiling-and-floor-functions
142
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Experiment:-$\sum_{j=1}^{2n+1}(j+1)\left\lfloor {j\cdot j!\over j+1} \right\rfloor$

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#sequences-and-series #proof-verification #prime-numbers #ceiling-and-floor-functions
270
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floor function: $\lfloor ax\rfloor-a\lfloor x\rfloor ≤ k$

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#calculus #functions #proof-writing #ceiling-and-floor-functions #analytic-spread
914
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Squaring a floor value

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#discrete-mathematics #ceiling-and-floor-functions
284
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Could $ \lfloor {\sqrt{n!}}\rfloor $ be a prime number?

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#prime-factorization #ceiling-and-floor-functions #primality-test
206
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Find the greatest integer not exceeding $A$ if $A = \sqrt{x^2+\sqrt{4x^2+\sqrt{16x^2+\sqrt{100x^2+39x+\sqrt{3}}}}}$ and $x=20062007$.

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#algebra-precalculus #ceiling-and-floor-functions #nested-radicals
118
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Equality using floor function

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#arithmetic #convex-analysis #ceiling-and-floor-functions
94
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How does one show that $\sum_{k=2}^{\infty}{(-1)^k\over k+1}\cdot{ \lceil \log_2(k) \rceil}=1-2\gamma?$

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#sequences-and-series #ceiling-and-floor-functions #euler-mascheroni-constant
2.7k
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Inverse of a floor function

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#calculus #functions #alternative-proof #ceiling-and-floor-functions #inverse-function
342
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Computing the integral $\int \limits_{1}^{\infty}\left(\frac{1}{\lfloor{x}\rfloor}-\frac{1}{x}\right)$ ....

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#limits #definite-integrals #ceiling-and-floor-functions #harmonic-numbers #euler-mascheroni-constant
330
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Solving A Simple Exponential floor Equation

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#ceiling-and-floor-functions
71
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Simplifying a Series with a lot of floors and ceilings

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#sequences-and-series #ceiling-and-floor-functions
168
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Identity related to the totient function:$\sum\limits_{k=1}^n\phi(k)\left\lfloor \frac{n}{k}\right\rfloor = \frac{n(n+1)}{2}$

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#number-theory #summation #ceiling-and-floor-functions #totient-function #arithmetic-functions

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