List questions from proof-explanation

57

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Lebesgue integral of $\int_\Omega fd\mu$ where $\mu(A)=\sum\limits_{k=1}^{n}\alpha_k\cdot\delta_{x_k}$

Published on 12 Apr 2026 - 1:08

67

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Why $\int_0^{\infty} f(t)dt = \lim_{\tau \to \infty }g_\tau (0)$?

Published on 15 Apr 2026 - 23:48

56

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Understanding steps in a proof.

Published on 10 Apr 2026 - 17:21

189

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Prove that $S(x) = \sum\limits_{n=1}^\infty \frac{\sin nx}{n\sqrt n}$ is convergent and can be differentiated on $x\in(0, 2\pi)$

Published on 15 Apr 2026 - 8:41

33

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Understanding the solution of a problem.

Published on 09 Apr 2026 - 10:07

90

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Show: $\sum_{n=1}^{k}\sum_{m=n}^{k}\int_m^{m+1}f(x)dx=\sum_{m=1}^{k}m \int_m^{m+1}f(x)dx$

Published on 17 Apr 2026 - 9:58

64

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Why is my idea of the expected value of the number of coin tosses wrong?

Published on 13 Apr 2026 - 23:45

182

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Why is Furch's "knotted hole ball" not shellable?

Published on 26 Mar 2026 - 4:30

344

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Proof of Edmund Landau's Foundation of Analysis

Published on 26 Mar 2026 - 12:48

190

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Reason why uniform convergence is required to $\zeta(s)$ is convergent?

Published on 14 Apr 2026 - 15:39

223

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Proof $a+a = 0$ by given $a\times a = a$

Published on 08 Apr 2026 - 16:21

662

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Understanding the Gram-Schmidt Procedure and Its Proof

Published on 06 Apr 2026 - 1:26

95

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Prove $\int(\phi+\psi)\,d\mu = \int\phi\,d\mu + \int\psi\,d\mu$

Published on 15 Apr 2026 - 5:21

58

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Explanation of the product rule for limits.

Published on 09 Apr 2026 - 4:42

78

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Apparent circularity of proofs for properties of natural number multiplication

Published on 22 Nov 2019 - 4:02

List Question

Lebesgue integral of $\int_\Omega fd\mu$ where $\mu(A)=\sum\limits_{k=1}^{n}\alpha_k\cdot\delta_{x_k}$

Why $\int_0^{\infty} f(t)dt = \lim_{\tau \to \infty }g_\tau (0)$?

Understanding steps in a proof.

Prove that $S(x) = \sum\limits_{n=1}^\infty \frac{\sin nx}{n\sqrt n}$ is convergent and can be differentiated on $x\in(0, 2\pi)$

Understanding the solution of a problem.

Show: $\sum_{n=1}^{k}\sum_{m=n}^{k}\int_m^{m+1}f(x)dx=\sum_{m=1}^{k}m \int_m^{m+1}f(x)dx$

Why is my idea of the expected value of the number of coin tosses wrong?

Why is Furch's "knotted hole ball" not shellable?

Proof of Edmund Landau's Foundation of Analysis

Reason why uniform convergence is required to $\zeta(s)$ is convergent?

Proof $a+a = 0$ by given $a\times a = a$

Understanding the Gram-Schmidt Procedure and Its Proof

Prove $\int(\phi+\psi)\,d\mu = \int\phi\,d\mu + \int\psi\,d\mu$

Explanation of the product rule for limits.

Apparent circularity of proofs for properties of natural number multiplication

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