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What is a composition of two binary relations geometrically?
the composition was defined as follow: (a,b) \in (R;S) <=> there is c | (a,c) \in R and (c,b) \in S . If our two relations R and S are two convex po...
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Monoid as a single object category
I'm struggling with comprehending what monoids are in terms of category theory. In examples they view integer numbers as a monoid. I think I get the ...
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How do you derive the backward differentiation formula of 3rd order using interpolating polynomials?
It was my exam question, and I could not answer it. How do you drive the backward differentiation formula of 3rd order (BDF3) using interpolating polynomi...
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Help with understanding Dedekind Cuts definition
I am trying to understand the definition of what a Dedekind Cut is and I get that these are subsets of the rationals that are non-empty not not the whole ...
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How should I calculate K in Rodrigues' rotation formula from the second order equation?
from Rodrigues' formula we know that : $$K^{2}\left ( 1 - \cos\varphi \right ) + K \sin{ \varphi} + I = R$$ we also know that $K$ should be $$K =\fra...
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What are primitive roots modulo n?
I'm trying to understand what primitive roots are for a given $\bmod\ n$. Wolfram's definition is as follows: A primitive root of a prime $p$ is...
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How to solve nested absolute value-equations?
Solving an equation like $|x-a| = 3$, is simple, where one just splits this into two equations for values of $x$ less than $a$ and values equal to or grea...
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Infinitely number of primes in the form $4n+1$ proof
Question: Are there infinitely many primes of the form $4n+3$ and $4n+1$? My attempt: Suppose the contrary that there exist finitely many primes of the fo...
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The difference between pointwise convergence and uniform convergence of functional sequences
$f_n$ converges pointwise to $f$ on $E$ if $\forall x \in E$ and $\forall \varepsilon > 0$, $\exists N \in \mathbb N$, such that $\forall n \geq N$ we ...
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Using calculus to determine how many roots are real
For the first one the calculus makes sense $f= x^3-3x+1$. So consider $f' = 3x^2 -3$ which has zeros at $\pm 1$. Then $f(1) = -3$ is negative and $f(...
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