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Advanced Inequality with Floor Functions

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#inequality #optimization #ceiling-and-floor-functions #cauchy-schwarz-inequality
84
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$Z$-transform of floor($\frac{n}{5}$)

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#ceiling-and-floor-functions #z-transform
652
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How to solve these inequalities with floors and ceilings?

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#inequality #ceiling-and-floor-functions
133
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Simpler ways of finding solutions to $\int_0^x \lfloor{x\rfloor}^2 dx=2(x-1)$

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#calculus #algebra-precalculus #definite-integrals #alternative-proof #ceiling-and-floor-functions
177
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Find a limit involving floor function

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#calculus #limits #ceiling-and-floor-functions
93
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Divide an integer in the sum of two integers with percentage factor using ceil and floor

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#solution-verification #integers #ceiling-and-floor-functions #integer-partitions
649
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How to solve $ \sum_{i=1}^{n} \left \lfloor{\log{i}}\right \rfloor $ for closed form

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#summation #logarithms #factorial #ceiling-and-floor-functions
124
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$[n \sqrt{2}] = [m (2+\sqrt{2})]$ for $m,n$ natural.

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#ceiling-and-floor-functions
24
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Graph of $(\lfloor(f(x))\rfloor)^2$

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#graphing-functions #ceiling-and-floor-functions
108
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Sum of the roots of $x^2-6[x]+6=0$, where $[.]$ is GIF

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#polynomials #ceiling-and-floor-functions
152
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Is there a simpler expression for this piecewise-defined function?

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#calculus #ceiling-and-floor-functions
129
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Sequence defined by recursive formula and floor function

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#sequences-and-series #contest-math #ceiling-and-floor-functions
137
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Find the probability that $[x+y+z]=[x]+[y]+[z]+2$

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#probability #solution-verification #ceiling-and-floor-functions
111
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Sequences and Greatest Integer Function

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#sequences-and-series #weak-convergence #ceiling-and-floor-functions #sequence-of-function
63
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Show that $\lceil n\cdot log_ab\rceil$ and $\lceil n\cdot log_\frac{b}{a}b\rceil$ "covers" all integers

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#number-theory #logarithms #ceiling-and-floor-functions

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