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What is a resolvent of an operator?
What is a resolvent $R$ of an operator $L$, and why do we care about it? $$R=(\lambda I-L)^{-1}.$$
Apr 19, 2026
Archive: Updates
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User DaCard - Mathematics Stack Exchange
Q&A for people studying math at any level and professionals in related fields
Apr 19, 2026
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small o(1) notation
It's probably a vey silly question, but I'm confused. Does o(1) simply mean $\lim_{n \to \infty} \frac{f(n)}{\epsilon}=0$ for some $n>N$?
Apr 19, 2026
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Proving Irrationality
How is it possible to prove a number is irrational? First part of that question: How it possible to know that a number will go on infinitely? Second part:...
Apr 19, 2026
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Flip Normal of Plane
Hi If I have a general form of a plane such as : $2x + 4y - 6z + 10 = 0$ what is the method for inverting the normal vector?? I realize the normal vector ...
Apr 19, 2026
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How to understand the combination formula?
I'm reading an algorithm book. In which it mentioned: Imagine (once again) you have n people lined up to see a movie, but there are only k places lef...
Apr 19, 2026
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What does "order matters" regarding permutations refer to?
I psychoanalyze EVERYTHING and permutations/combinations are frustrating me. Sorry for posting so many questions lately but I really appreciate all of the...
Apr 19, 2026
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Using Cauchy's Inequality to prove a function's second derivative is zero
Let $f$ be an entire function (i.e. analytic everywhere, i.e. holomorphic) such that $\left\vert f(z) \right\vert \leq A \left\vert z \right\vert$, $\fora...
Apr 19, 2026
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Definition of Unsigned Definite Integral
In Terence Tao's paper Differential Forms and Integration, he mentions that there are $3$ distinct notions of integration when discussing functions $...
Apr 19, 2026
![IMO 1987 - function such that $f(f(n))=n+1987$ [closed]](https://news.conceivablytech.com/uploads/imo-1987-function-such-that-f-f-n-n-1987-closed_720.jpg)
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IMO 1987 - function such that $f(f(n))=n+1987$ [closed]
Show that there is no function $f: \mathbb{N} \to \mathbb{N}$ such that $$f(f(n))=n+1987, \ \forall n \in \mathbb{N}$$ This is problem 4 from IMO 1987 - s...
Apr 19, 2026
