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15
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Graph of $f(x)=x-[x]-\dfrac{1}{2}$

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#calculus #ceiling-and-floor-functions
76
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Solve Inequality with ceiling function.

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#elementary-number-theory #inequality #ceiling-and-floor-functions
196
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Algorithm to find floors of multiples of the golden ratio

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#algorithms #integers #ceiling-and-floor-functions #continued-fractions #golden-ratio
99
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Values of $x$ satisfying $\lfloor{x^2\rfloor}=\left(\lfloor{x\rfloor}\right)^2$

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#algebra-precalculus #functions #inequality #ceiling-and-floor-functions
86
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Proving $\int_0^{n^2} \left\lfloor\sqrt t\right\rfloor \,dt=\frac{n(n-1)(4n+1)}{6}$

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#calculus #ceiling-and-floor-functions
311
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Doubt on Integration

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#calculus #definite-integrals #ceiling-and-floor-functions #fractional-part
106
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Showing $\int_{a}^{b} \left\lfloor x \right\rfloor dx + \int_{a}^{b} \left\lfloor -x \right\rfloor dx=a-b$

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#calculus #ceiling-and-floor-functions
85
Views

Reasoning about inequalities involving floor functions

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#proof-verification #inequality #induction #ceiling-and-floor-functions
92
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Approximating series of fractions

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#sequences-and-series #summation #radicals #ceiling-and-floor-functions #telescopic-series
193
Views

Chebyshev function - show that $\psi(x)>(x-2)\log2-\log(x+1)$

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#number-theory #elementary-number-theory #ceiling-and-floor-functions #chebyshev-function
210
Views

Proving that the $\lfloor-x\rfloor= -\lceil x\rceil$

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#algebra-precalculus #elementary-number-theory #ceiling-and-floor-functions
69
Views

I need to solve one equation, but I dont know how to solve equation with floor functions

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#proof-verification #binary #ceiling-and-floor-functions #binary-operations
155
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Divergence of a sequence with floors and square roots $a_n = n\sqrt2 - [n\sqrt2] + n\sqrt3 -[n\sqrt3]$

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#real-analysis #sequences-and-series #convergence-divergence #radicals #ceiling-and-floor-functions
48
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Ceiling function inequality mistake in an article?

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#inequality #ceiling-and-floor-functions
83
Views

Is $\lfloor2\sqrt{n-\lfloor \sqrt{n} \rfloor}\rfloor <\lfloor2\sqrt{n} \rfloor$ true for $n\geq 0$?

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#discrete-mathematics #inequality #real-numbers #ceiling-and-floor-functions

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