List questions from solution-verification

Published on 17 Apr 2026 - 10:23

101

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Proof that the sequence defined by the average of the last two terms is convergent.

Published on 12 Apr 2026 - 19:21

137

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Find the density of $\cos(X)$ when $X$ is an exponential.

Published on 11 Apr 2026 - 12:51

32

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Let $f: A\rightarrow B, g: B\rightarrow C, and h: C\rightarrow D$. If $f$ and $g$ are both injective, then $g\circ f$ is injective.

Published on 16 Apr 2026 - 8:53

65

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Prove $f(x)=\int_{-1}^{x}\sin{(xt)e^{-t^2}}dt$ is uniformly continuous on $I=[0,\infty)$ (Proof Verification)

Published on 14 Apr 2026 - 2:24

51

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Where is the hypothesis that $f_{n-1}(x, y)+f_n(x, y)$ is irreducible used in my solution?

Published on 13 Apr 2026 - 8:33

21

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The coordinate map of a one-dimensional TVS is continuous

Published on 10 Apr 2026 - 23:30

97

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Show that a convergent sequence exists within any uncountable set of reals

Published on 14 Apr 2026 - 8:25

41

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Uniqueness-proof

Published on 15 Apr 2026 - 20:01

185

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Why is a Countable Basis Needed in This Proof?

Published on 10 May 2026 - 19:49

42

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Linearity of Lebesgue integral in the complex case.

Published on 12 Apr 2026 - 13:41

22

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If $x_d \to 0_E$ and $\sup_{d\in D} |\lambda_d| <\infty$, then $\lambda_d x_d \to 0_E$

Published on 14 Apr 2026 - 18:55

30

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Does the given symmetry help to prove that the region in which conditions $\textbf{cond.1}$ and $\textbf{cond.2}$ hold is the same?

Published on 13 Apr 2026 - 20:46

98

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Let $H,K \leq G$ s.t $H,K$ two different Sylow $p$-subgroups of $G$. Prove $HK$ isn't a subgroup of $G$.

Published on 15 Apr 2026 - 6:46

73

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Is $G/ \gamma_n(G)$ nilpotent for every $n \in \mathbb{N}$?

Published on 15 Apr 2026 - 8:34

List Question

Evaluating $\int_{0}^{1}\frac{\arctan(x)}{x^2+x+1}\,dx$

Proof that the sequence defined by the average of the last two terms is convergent.

Find the density of $\cos(X)$ when $X$ is an exponential.

Let $f: A\rightarrow B, g: B\rightarrow C, and h: C\rightarrow D$. If $f$ and $g$ are both injective, then $g\circ f$ is injective.

Prove $f(x)=\int_{-1}^{x}\sin{(xt)e^{-t^2}}dt$ is uniformly continuous on $I=[0,\infty)$ (Proof Verification)

Where is the hypothesis that $f_{n-1}(x, y)+f_n(x, y)$ is irreducible used in my solution?

The coordinate map of a one-dimensional TVS is continuous

Show that a convergent sequence exists within any uncountable set of reals

Uniqueness-proof

Why is a Countable Basis Needed in This Proof?

Linearity of Lebesgue integral in the complex case.

If $x_d \to 0_E$ and $\sup_{d\in D} |\lambda_d| <\infty$, then $\lambda_d x_d \to 0_E$

Does the given symmetry help to prove that the region in which conditions $\textbf{cond.1}$ and $\textbf{cond.2}$ hold is the same?

Let $H,K \leq G$ s.t $H,K$ two different Sylow $p$-subgroups of $G$. Prove $HK$ isn't a subgroup of $G$.

Is $G/ \gamma_n(G)$ nilpotent for every $n \in \mathbb{N}$?

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