List questions from proof-explanation

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Every graph $G$ with $d(G) \ge 4k$ has a $(k + 1)$-connected subgraph $H$ such that $\epsilon (H) > \epsilon(G) − k$.

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Every maximal ideal of a commutative unitary ring is prime (Proof explanation)

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(Proof explanation) In integral domain let there be a prime ideal $(a)$ then $a$ is irreducible.

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How does the next step conclude from the previous one?

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How to prove each column vector $t^i$ of $\Bbb{R}^n$ satisfies $At^i = \lambda(t^i)$?

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List Question

Double negation vs. law of excluded middle?

Munkres, Theorem 16.4

Abstract Algebra: Prove if it is an abelian group. Need Clarification

Prove: $ \left\langle \preccurlyeq,P_{\aleph_{0}}(\mathbb{N})\right\rangle $ is a Partially ordered set

Modus ponens as a rule of inference vs. tautology

On Understanding A Proof On The Fact That Differentiability Implies Continuity

Questions about the Proof that $\inf A = - \sup\left(-A\right)$ (Rudin)

Every graph $G$ with $d(G) \ge 4k$ has a $(k + 1)$-connected subgraph $H$ such that $\epsilon (H) > \epsilon(G) − k$.

Every maximal ideal of a commutative unitary ring is prime (Proof explanation)

(Proof explanation) In integral domain let there be a prime ideal $(a)$ then $a$ is irreducible.

About the proof that $\int_0^\infty\frac{dx}{x^2+6x+8} =\frac12\log2$ via residue formula

Proving that $\mathbb{Q}[X] = (X-1) + (X+1)$

What are the most popular techniques of proving inequalities?

How does the next step conclude from the previous one?

How to prove each column vector $t^i$ of $\Bbb{R}^n$ satisfies $At^i = \lambda(t^i)$?

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