List questions from proof-writing

Published on 01 Apr 2026 - 7:22

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Hölder continuous functions are uniformly continuous

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Prove that induction to all $n$ it is natural that $a_n$ is irrational and positive number.

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Is this Theorem equivalent to Axiom of Choice?

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Prove that Axiom of Dependent Choice implies Axiom of Countable Choice

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Top-down proof of a lemma used in Schröder-Bernstein theorem

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If $a\mid b$ and $a>0$ then $(a,b)=a$

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Suppose that $Z \subseteq Y \subseteq X$ and that $f:X \to Z$ is bijective. Then $A$ is the minimal element of $\mathcal{F}$

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Proving existence of basis that can be constructed using Jordan Blocks.

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A general formula for the second degree derivative?

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Prove $N\cdot lg(N) = \sum_{k=1}^N(\lfloor lg(k) \rfloor + 2)$ - "Analysis of Algorithms" by R. Sedgewick

Published on 25 Mar 2026 - 13:57

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Understanding Analysis (Abbott) Lemma 1.3.7; is my proof correct?

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One-to-One and Onto Proof

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If $f(x)$ is convex on $[a,b]$, show $h(x) = \frac{f(x) - f(a)}{x - a}$ is increasing

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Baire space - probably a typo in the book

Published on 03 Apr 2026 - 22:38

List Question

Julius König's proof of Schröder–Bernstein theorem

Hölder continuous functions are uniformly continuous

Prove that induction to all $n$ it is natural that $a_n$ is irrational and positive number.

Is this Theorem equivalent to Axiom of Choice?

Prove that Axiom of Dependent Choice implies Axiom of Countable Choice

Top-down proof of a lemma used in Schröder-Bernstein theorem

If $a\mid b$ and $a>0$ then $(a,b)=a$

Suppose that $Z \subseteq Y \subseteq X$ and that $f:X \to Z$ is bijective. Then $A$ is the minimal element of $\mathcal{F}$

Proving existence of basis that can be constructed using Jordan Blocks.

A general formula for the second degree derivative?

Prove $N\cdot lg(N) = \sum_{k=1}^N(\lfloor lg(k) \rfloor + 2)$ - "Analysis of Algorithms" by R. Sedgewick

Understanding Analysis (Abbott) Lemma 1.3.7; is my proof correct?

One-to-One and Onto Proof

If $f(x)$ is convex on $[a,b]$, show $h(x) = \frac{f(x) - f(a)}{x - a}$ is increasing

Baire space - probably a typo in the book

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