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How to calculate the norm of an ideal?

Would someone please help explain how to calculate the norm of an ideal? I can't find a source that explains this clearly. For example, I know that t...

Published: Aug 25, 2026

$Help with using Euler’s formula to prove that $\cos^2(\theta) = \frac{\cos(2\theta)+1}{2}$$

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Help with using Euler’s formula to prove that $\cos^2(\theta) = \frac{\cos(2\theta)+1}{2}$

I have to use Euler's Formula to prove that: $$\cos^2(\theta) = \frac{\cos(2\theta)+1}{2}.$$ I have managed to prove this using trigonometric identit...

Published: Aug 25, 2026

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Question about an isometric immersion

This is the question: Let $M,N$ be Riemannian manifolds, such that the inclusion $i:M \to N$ is a isometric immersion. Give a example where the inequality...

Published: Aug 25, 2026

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Complex Number solutions for a Circle

I have a circle of radius 5 with its center at the origin represented as $X^2+Y^2=25$. I get that it has a solution for all values ranging from $-5$ to $+...

Published: Aug 25, 2026

$Is there a pythagorean triple such that all angles of the corresponding triangle are simple fractions of $\pi$?$

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Is there a pythagorean triple such that all angles of the corresponding triangle are simple fractions of $\pi$?

Obviously, the most interesting pythagorean triple $(a, b, c)$ would be one for which the corresponding triangle (with integer side lengths $a, b, c$) has...

Published: Aug 25, 2026

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What is the output of a function which is not defined for input = 0 (for example because of the division by zero) if we give zero to this function? [closed]

My teacher told me that every function has to be able to assign an output to every input we give to this function. What is than an output for a function w...

Published: Aug 25, 2026

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Hatcher and "house with two rooms"

On page 4 of Hatcher's "Algebraic Topology" he constructs the "house with two rooms" space. He claims that there is some neighborhood containing this...

Published: Aug 25, 2026

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Proof verification for proof by contraposition

prove using contraposition that if a and b are integers: $a^2-4b-2\neq0$ So the contrapositive: $a^2-4b-2=0$ implies that at least one of either a or b ar...

Published: Aug 25, 2026

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How to calculate 15! without using calculator

I am joining a maths competition and recently I am preparing for it. I came across a question that asks me to fill the blank of a number: 1_0767436_000 An...

Published: Aug 25, 2026

$Why is $y = \sqrt{x-4}$ a function? and $y = \sqrt{4 - x^2}$ should be a circle$

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Why is $y = \sqrt{x-4}$ a function? and $y = \sqrt{4 - x^2}$ should be a circle

So why is it a function, even though for example $x = 8$; you'll have $y = +2$ and $y = -2$. It'll fail the vertical line test. But every textbo...

Published: Aug 25, 2026

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