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Limit involving floor function: $\lim\limits_{x\to 0} x \left\lfloor\frac1x \right\rfloor$

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#calculus #limits #ceiling-and-floor-functions
129
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Closed form of finite sum involving the floor function

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#sequences-and-series #discrete-mathematics #summation #ceiling-and-floor-functions
183
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Is $\lim\limits_{n\to\infty}(A_{n+1}-A_{n})$ finite?

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#sequences-and-series #dynamical-systems #ceiling-and-floor-functions #iterated-function-system
131
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How to solve a linear system of equation with floor function?

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#linear-algebra #matrices #ceiling-and-floor-functions #gaussian-elimination
113
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Is it true that $\lim_{n \to \infty } nt - \lfloor nt \rfloor =0 $?

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#calculus #limits #ceiling-and-floor-functions
153
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Continous, Non-Fourier, Trigonometric Approximation of the Floor Function

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#functions #trigonometry #ceiling-and-floor-functions
307
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Rewriting the Floor function in terms of the Heaviside Step Function and/or Sign Function

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#functions #approximation #ceiling-and-floor-functions #fractional-part
208
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Find $n$ such that $n\sqrt5 - \lfloor{n\sqrt5}\rfloor$ is maximised or minimised?

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#number-theory #contest-math #ceiling-and-floor-functions
122
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Equation involving floor function without real solutions

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#real-analysis #algebra-precalculus #contest-math #ceiling-and-floor-functions
1.8k
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Log Laws with Ceiling and Floor Function

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#logarithms #ceiling-and-floor-functions
67
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Questions on The Sum and Difference of Floor Functions

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#ceiling-and-floor-functions
59
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A Tricky Partition of Natural Numbers

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#ceiling-and-floor-functions #natural-numbers
104
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Sum of Squares of Floor Function

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#summation #ceiling-and-floor-functions
130
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Pairs into segments which do not intersect.

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#combinatorics #contest-math #ceiling-and-floor-functions
770
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Closed expression for sum $\sum_{k=1}^{\infty} (-1)^{k+1}\frac{\left\lfloor \sqrt{k}\right\rfloor}{k}$

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#sequences-and-series #closed-form #ceiling-and-floor-functions

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