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Why is $\{x/2\}$ always either $\{x\}/2$ or $\{x\}/2 + 1/2$?

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#ceiling-and-floor-functions #fractional-part
35
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Finding the greatest integer by guessing root of a polynomial

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#inequality #roots #ceiling-and-floor-functions
103
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Solve the equation: $\frac{x^2 - 2x + 3}{\lbrace x\rbrace} + \frac{2023}{2}{\lbrace x\rbrace} = 2\lfloor x \rfloor + 88$

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#algebra-precalculus #quadratics #ceiling-and-floor-functions #fractional-part
120
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Monster floor integral from the $2023$ MIT Integration Finals: $\int_0^1\left(\sum_{n=1}^\infty\frac{\lfloor2^nx\rfloor}{3^n}\right)^2dx$

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#integration #solution-verification #summation #ceiling-and-floor-functions
146
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An interesting integral $\int_0^{\infty}\{e^x\}-\frac {1}{2}dx$

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#calculus #integration #sequences-and-series #definite-integrals #ceiling-and-floor-functions
157
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I found a really interesting sum involving the floor function. Can someone help explain why it works the way it does?

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#sequences-and-series #limits #convergence-divergence #ceiling-and-floor-functions
203
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Evaluate the limit $\lim_{n\to \infty }\sum_{i=1}^n \frac{1}{n} \cdot \lfloor \sqrt {\frac{4i}{n}} \rfloor$

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#calculus #limits #riemann-integration #ceiling-and-floor-functions #riemann-sum
128
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I came up with a proof for a Putnam Question, and I would appreciate feedback or direction to a resource that would give feedback.

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#real-analysis #sequences-and-series #contest-math #ceiling-and-floor-functions
87
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Where is $g(x)=x\lfloor x+1 \rfloor$ continuous?

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#real-analysis #limits #analysis #continuity #ceiling-and-floor-functions
178
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$p = s(\left \lfloor t\right \rfloor+\frac{\sin(\frac{\pi\left \lfloor t\right \rfloor}{t})}{\sin(\frac{\pi}{t})})$ , make $t$ the subject?

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#trigonometry #ceiling-and-floor-functions
235
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Why does limit: $\lim_{x\to\infty}\prod\limits^{\lfloor x\rfloor}_{n=1}\frac{\lceil x\rceil}{\lfloor x\rfloor}=e$?

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#real-analysis #sequences-and-series #limits #ceiling-and-floor-functions #infinite-product
108
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Can floor(floor(a/b)/c) ever be different to floor(a/(bc))?

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#ceiling-and-floor-functions
72
Views

How to solve function with floor: $a\left(\big \lfloor\frac {a} {2\pi}\big \rfloor + 1\right) = 100$

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#ceiling-and-floor-functions
88
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Methods to prove statements with floor (or ceiling) expressions?

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#proof-writing #induction #alternative-proof #ceiling-and-floor-functions
66
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Is this result about the floor function true?

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#ceiling-and-floor-functions

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