List questions from real-analysis

Published on 16 Apr 2026 - 7:05

177

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Why do we need $\beta_1>0$ and $\alpha_n<\beta_n$ in this proof?

Published on 15 Apr 2026 - 7:24

43

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Uniform convergence of $f_n(x)=\frac{n^a x^{n-3/2}}{1+x^n}$, $a\in R^+, x \in (0,1)$

Published on 17 Apr 2026 - 9:11

57

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Limit of a boundary of increasing sequence of sets

Published on 13 Apr 2026 - 17:40

420

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Bijective compact operator between $X$ and $Y$ with $\text{dim}(X)=\infty$?

Published on 02 May 2026 - 20:27

191

Views

Trajectories in circular Billards

Published on 30 Apr 2026 - 19:08

2k

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Show that $f(n)=n^3+20n+1=O(n^3)$

Published on 17 Apr 2026 - 11:06

155

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Supremum and infimum in subsets of $\mathbb{R^+}$

Published on 12 Apr 2026 - 21:06

104

Views

A refinement of a difficult inequality involving reciprocal gamma function

Published on 13 Apr 2026 - 21:15

167

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Uniform continuity of the CDF of a continuous Random variable.

Published on 14 Apr 2026 - 3:55

69

Views

What is $(1 + O(h))^{-1}$?

Published on 12 Apr 2026 - 23:51

468

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Show that partial sums of a function converge pointwise but not uniformly

Published on 29 Apr 2026 - 12:54

155

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Prove Borel-Cantelli's lemma

Published on 29 Apr 2026 - 12:24

54

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Equivalence definitions of limits of a sequence

Published on 10 Apr 2026 - 20:14

688

Views

Integral $\int_0^\infty e^{-x^2} \cos\alpha x \ dx$

Published on 17 Apr 2026 - 3:22

List Question

Show that $\frac1x+\log x-\log(x+1)\ge0$ for $x\ge1$ without differential calculus

Why do we need $\beta_1>0$ and $\alpha_n<\beta_n$ in this proof?

Uniform convergence of $f_n(x)=\frac{n^a x^{n-3/2}}{1+x^n}$, $a\in R^+, x \in (0,1)$

Limit of a boundary of increasing sequence of sets

Bijective compact operator between $X$ and $Y$ with $\text{dim}(X)=\infty$?

Trajectories in circular Billards

Show that $f(n)=n^3+20n+1=O(n^3)$

Supremum and infimum in subsets of $\mathbb{R^+}$

A refinement of a difficult inequality involving reciprocal gamma function

Uniform continuity of the CDF of a continuous Random variable.

What is $(1 + O(h))^{-1}$?

Show that partial sums of a function converge pointwise but not uniformly

Prove Borel-Cantelli's lemma

Equivalence definitions of limits of a sequence

Integral $\int_0^\infty e^{-x^2} \cos\alpha x \ dx$

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