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Finding the maximum value for $\left\lceil\frac{b-x}{2}\right\rceil + \left\lceil\frac{x-a}{2}\right\rceil$

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#functions #optimization #ceiling-and-floor-functions
793
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Mathematical equivalents of bitwise AND, OR, and XOR operators

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#summation #solution-verification #ceiling-and-floor-functions #bit-strings
529
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A question about sizes of antichains

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#combinatorics #elementary-set-theory #ceiling-and-floor-functions #extremal-combinatorics
362
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Proof relating to square root and floor function

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#elementary-number-theory #solution-verification #ceiling-and-floor-functions
72
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If $k\geq3$ then $\binom{\lfloor2^{k/2}\rfloor}{k}2^{1-\binom{k}{2}}<1$.

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#number-theory #inequality #binomial-coefficients #ceiling-and-floor-functions
33
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How to prove that $x\lfloor\frac{a}{x+1}\rfloor\geq \lfloor\frac{a}{2}\rfloor$, where $a\geq2$, $1\leq x\leq a-1$， $a$ and $x$ are integers.

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#ceiling-and-floor-functions
160
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How to prove that $\lceil\lceil x/a\rceil/b\rceil=\lceil x/(ab)\rceil\;\;\forall\text{ real }x\geq0\text{ , }\forall\text{ integer }a,b>0$

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#ceiling-and-floor-functions
49
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⌊3/x⌋ + ⌊4/x⌋ = 5

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#ceiling-and-floor-functions
82
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Doubts about this nicely integral identity with floor function

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#calculus #sequences-and-series #definite-integrals #ceiling-and-floor-functions
62
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How to solve for the inverse of $f$ for a floor function? I really need to learn the method.

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#functions #discrete-mathematics #ceiling-and-floor-functions #inverse-function #inverse-problems
45
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A complex recurrence relation

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#recurrence-relations #recursion #ceiling-and-floor-functions
124
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What do you call this generalized floor function?

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#functions #maxima-minima #ceiling-and-floor-functions #rounding-unit
291
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Valid application of integration by parts for piecewise functions

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#real-analysis #calculus #integration #definite-integrals #ceiling-and-floor-functions
110
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How to simplify this equation?

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#elementary-number-theory #inequality #ceiling-and-floor-functions
204
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Olympiad question involving divisibility and floor function

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#contest-math #divisibility #ceiling-and-floor-functions

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