List questions from proof-writing

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How to get the value of the expression?

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Co-Countable topology cases

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How to prove the directed angle cyclic quadrilateral theorem?

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128

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How to get the maximum of $f(x,y,z)=\frac{x+\sqrt{xy}+\sqrt[3]{xyz}}{x+y+z}, x,y,z\in\mathbb{R}_+$

Published on 15 Apr 2026 - 12:54

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Prove the following for an addition binary operation

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Interior topology

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Prove that If $a$ and $b$ are real numbers with $a < b < 0$ then $a^2 > b^2$

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Prove that if $a$ and $b$ are real numbers with $0 < a < b$ then $\frac{1}{b} < \frac{1}{a}$

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Prove that $\sin(x)$ is locally invertible, whereas $\tan(x)$ is globally invertible on its domain

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Prove that if $a$ is a real number and $a^3 > a$ then $a^5 > a$

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Is it acceptable to write "the function $f_n$ is cts for every $n \in \mathbb{N}$"?

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Suppose 1 ≤ k ≤ n − 1 and gcd(k, n) = 1. Prove that gcd(n − k, n) = 1

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Prove the following for a general binary operation, $\Delta$

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Prove that it cannot be proven that "The United States had more fallow acreage than planted acreage"

Published on 15 Apr 2026 - 6:36

List Question

Complete treatment of Vitali set.

How to get the value of the expression?

Co-Countable topology cases

How to prove the directed angle cyclic quadrilateral theorem?

How to get the maximum of $f(x,y,z)=\frac{x+\sqrt{xy}+\sqrt[3]{xyz}}{x+y+z}, x,y,z\in\mathbb{R}_+$

Prove the following for an addition binary operation

Interior topology

Prove that If $a$ and $b$ are real numbers with $a < b < 0$ then $a^2 > b^2$

Prove that if $a$ and $b$ are real numbers with $0 < a < b$ then $\frac{1}{b} < \frac{1}{a}$

Prove that $\sin(x)$ is locally invertible, whereas $\tan(x)$ is globally invertible on its domain

Prove that if $a$ is a real number and $a^3 > a$ then $a^5 > a$

Is it acceptable to write "the function $f_n$ is cts for every $n \in \mathbb{N}$"?

Suppose 1 ≤ k ≤ n − 1 and gcd(k, n) = 1. Prove that gcd(n − k, n) = 1

Prove the following for a general binary operation, $\Delta$

Prove that it cannot be proven that "The United States had more fallow acreage than planted acreage"

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