List questions from proof-writing

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Can a valid proof by contradiction contradict the opposite proposition?

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Understanding the proof a metrizable connected space has uncountable elements if $|X|\geqslant 2$

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Inductive proof verification

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Proof that if $\sqrt {ab}$ is rational then $\sqrt {\frac{a}{b}}$ is also rational.

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Closed sets in infinite product topological spaces

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Proof that $e^{ab} = \left(e^a\right)^b$, using the series for $e^x$

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Proving $A \in B \land B \subseteq C \to A \in C$.

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Consider the function $θ:\{0,1\}×{\Bbb N}→{\Bbb Z}$ defined as $θ(a,b)=(-1)^{a}b$

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Prove that for all integers $x$ with final digit equal to $5$, $x$ is a multiple of $5$

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prove or disprove (K ∩ L) × (M ∩ N) = (K × M) ∩ (L × N);

Published on 16 Apr 2026 - 18:49

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Proving finite bases for a Harshad number?

Published on 15 Apr 2026 - 21:17

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Strong induction and vacuous truth

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If $f$ is the quotient mapping, is $(Y,\tau_1)$ metrizable?

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Show that if $\lim_{n \to \infty} x_n = 0$ if follows that $\lim_{n \to \infty} (1+\frac{x_n}{n})^n = 1$

Published on 16 Apr 2026 - 9:33

List Question

How to give formal proof in logic?

Can a valid proof by contradiction contradict the opposite proposition?

Understanding the proof a metrizable connected space has uncountable elements if $|X|\geqslant 2$

Inductive proof verification

Proof that if $\sqrt {ab}$ is rational then $\sqrt {\frac{a}{b}}$ is also rational.

Closed sets in infinite product topological spaces

Proof that $e^{ab} = \left(e^a\right)^b$, using the series for $e^x$

Proving $A \in B \land B \subseteq C \to A \in C$.

Consider the function $θ:\{0,1\}×{\Bbb N}→{\Bbb Z}$ defined as $θ(a,b)=(-1)^{a}b$

Prove that for all integers $x$ with final digit equal to $5$, $x$ is a multiple of $5$

prove or disprove (K ∩ L) × (M ∩ N) = (K × M) ∩ (L × N);

Proving finite bases for a Harshad number?

Strong induction and vacuous truth

If $f$ is the quotient mapping, is $(Y,\tau_1)$ metrizable?

Show that if $\lim_{n \to \infty} x_n = 0$ if follows that $\lim_{n \to \infty} (1+\frac{x_n}{n})^n = 1$

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