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Proving That Limit of Greatest Integer Function Does Not Exist using Epsilon-Delta

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#real-analysis #limits #analysis #epsilon-delta #ceiling-and-floor-functions
49
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Proof for a non strictly increasing sequence

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#sequences-and-series #solution-verification #ceiling-and-floor-functions
146
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Solving a system like $\lfloor x / a_i \rfloor = b_i \pmod M$

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#modular-arithmetic #systems-of-equations #ceiling-and-floor-functions #integer-programming
48
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Using the Least Upper Bound Property to prove a condition

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#real-analysis #supremum-and-infimum #ceiling-and-floor-functions
44
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Bounding ceiling functions

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#inequality #upper-lower-bounds #ceiling-and-floor-functions
57
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How to solve equations involving floor function

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#discrete-mathematics #ceiling-and-floor-functions
67
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$\sum_{k = 1}^{\infty} k\lfloor\frac{n}{k} \rfloor = 1 + \sum_{k = 1}^n \sigma_1(n)$

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#sequences-and-series #elementary-number-theory #ceiling-and-floor-functions #divisor-sum #arithmetic-functions
193
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Evaluate the definite integral $\int_0^1 \lfloor \log_{2023}(x) \rfloor dx$

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#calculus #integration #sequences-and-series #solution-verification #ceiling-and-floor-functions
104
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Find the roots of a quadratic equation, with integer coefficients, rounded to nearest integer

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#roots #arithmetic #quadratics #ceiling-and-floor-functions
70
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Closed form of sum with ceil of logarithm.

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#discrete-mathematics #summation #logarithms #ceiling-and-floor-functions
72
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Prove that for any $n>2$, $n \in \Bbb N$, $\lfloor (\sqrt[3]{n}-\sqrt[3]{n+2})^3 \rfloor \equiv -1 \mod \ 8$

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#elementary-number-theory #ceiling-and-floor-functions
103
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A characterization of the floor function

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#functional-equations #ceiling-and-floor-functions #fractional-part
83
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Proof that the function $f(x)=x(\frac{3}{2}+\lfloor -x^2 \rfloor)$ is injective

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#functions #ceiling-and-floor-functions
117
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What is this "periodic" sequence called?

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#sequences-and-series #modular-arithmetic #logarithms #exponentiation #ceiling-and-floor-functions
51
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Why does any $\lfloor x+yi\rfloor\gets\lfloor x\rfloor+\lfloor yi\rfloor$?

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#complex-numbers #modular-arithmetic #ceiling-and-floor-functions

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