Thursday, January 9, 2020

analysis - Injection, making bijection

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I have injection $f \colon A \rightarrow B$ and I want to get bijection. Can I just resting codomain to $f(A)$? I know that every function i...

sequences and series - How do you prove $sum_{n=0}^infty frac{(-1)^n}{n!} = frac{1}{e}$?

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prove the sum $$\sum_{n=0}^\infty \frac{(-1)^n}{n!} = \frac{1}{e}$$ In one of the solutions to a problem I was looking at had this sum and d...
Wednesday, January 8, 2020

Discarding random variables in favor of a domain-less definition?

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Probabilists don't care, what exactly the domain of random variables is. Here is an extreme comment that exemplifies this: "You sh...

logarithms - Inequality $log xle frac{2}{e} , sqrt{x}$

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The inequality $$\log x \le \frac{2}{e} \, \sqrt{x},$$ where $\log x$ denotes the natural logarithm , is used in the proof of Theorem 4.7 i...

real analysis - How can you prove that a function has no closed form integral?

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I've come across statements in the past along the lines of "function $f(x)$ has no closed form integral", which I assume mean...

abstract algebra - Greatest common divisor of polynomials over $mathbb{Q}$

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I have two polynomials: $f: x^3 + 2x^2 - 2x -1$ and $g: x^3 - 4x^2 + x + 2$. I have to do two things: find $gcd(f,g)$ and find polynomials $...

gcd and lcm - using extended euclidean algorithm to find s, t, r

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i am stuck for many hours and i don't understand using the extended euclidean algorithm. i calculated it the gcd using the regular algor...