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Why does "per" translate into devision in math?
For example, when we want to represent speed, measured in meters per second, we are taught to write it as m/s , but why exactly do we divide meters (m) by...
Apr 18, 2026
Archive: News
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How do I convert a percentage from a 1%-100% scale to a different scale?
So if I have 9%, and this 9% fits in where 0 is the lowest and 100% is the highest, what would that 9% be if 25% is the lowest and 75% is the highest? Wha...
Apr 18, 2026
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Prove: $(a^{-1})^{-1}=a$ Over A Field
let $0\neq a\in \mathbb{F}$ Prove: $$(a^{-1})^{-1}=a$$ I have tried to start with the definition of an inverse, For all $0\neq a\in \mathbb{F}$ we have: $...
Apr 18, 2026
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What does it mean to say that a function is integrable with respect to a measure?
What does it mean to say a measurable function is integrable with respect to a measure, such as $\mu$? I know the definition of integrability, but I'...
Apr 18, 2026
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Odd/Even Permutations
How do you classify a permutation as odd or even (composition of an odd or even number of transpositions)? I somewhat understand the textbook definition o...
Apr 18, 2026
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Integration of the cardinal sine
It is said that the integral of the cardinal sine is $1$. How do I integrate the cardinal sine? $$ \int_{-\infty}^{\infty} \frac{\sin(a)}{a} \, {\rm d} a $$
Apr 18, 2026
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Zeroes of the Fourier transform of bump functions
$f(x)$ is a 1D bump function which real, even and compactly supported in the interval $[-a,a]$, and strictly positive within that interval. Are there any ...
Apr 18, 2026
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Lower bounds on the number of edges in a nonplanar graph
Let $e$ be the number of edges and $v \geq 3$ the number of vertices in a graph $G$. We know that if $G$ is planar, then $e \leq 3v-6$. My question is the...
Apr 18, 2026
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Good books and lecture notes about category theory.
What are the best books and lecture notes on category theory?
Apr 18, 2026
![Conditional expectation (order statistics and sample mean) [closed]](https://news.conceivablytech.com/uploads/conditional-expectation-order-statistics-and-sample-mean-closed_720.jpg)
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Conditional expectation (order statistics and sample mean) [closed]
How does one calculate the following: Given $X_1,...,X_n$ are i.i.d. uniform random variables, calculate $E[X_1|X_{(n)}]$ where $X_{(n)}$ denotes the $n^{...
Apr 18, 2026
