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Smart tricks used to prove formulas by approximation

score 81 · Answer 1 · 2026-03-25 04:37:28

81

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Smart tricks used to prove formulas by approximation

Published on 25 Mar 2026 - 4:37

score 308 · Answer 2 · 2018-04-21 05:23:25

308

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Suppose that $f$ has the property that $f(x+y)=f(x)+f(y)$.

Published on 21 Apr 2018 - 5:23

score 271 · Answer 3 · 2026-04-13 02:12:00

271

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The Mean Value Theorem (inequality) for complex-valued functions of several real variables

Published on 13 Apr 2026 - 2:12

score 35 · Answer 4 · 2018-04-21 09:23:22

35

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Showing $h(t):=( s \mapsto\frac{s}{s+2+t})$ is continuous and calculating $\int_{-1}^1h(t)dt$.

Published on 21 Apr 2018 - 9:23

score 41 · Answer 5 · 2026-04-11 15:19:32

41

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If $A\leq \mathbb{Z}$ then $\sup A\in A$

Published on 11 Apr 2026 - 15:19

score 1.1k · Answer 6 · 2026-04-10 17:46:03

1.1k

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Integral of holomorphic function is again holomorphic

Published on 10 Apr 2026 - 17:46

score 39 · Answer 7 · 2026-04-09 18:04:47

39

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Does a sequence of derivatives takes on its limiting value?

Published on 09 Apr 2026 - 18:04

score 111 · Answer 8 · 2026-04-12 15:32:50

111

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Continuous functions approximating identity

Published on 12 Apr 2026 - 15:32

score 225 · Answer 9 · 2018-04-21 23:11:30

Let $x_n = \sum_{ j=1}^n \frac1j$. Show that for every $k$ we have $\lim _{n→∞} |xn+k −xn| = 0$, yet {$x_n$} is not Cauchy.

score 56 · Answer 10 · 2026-04-09 01:48:57

56

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Different forms of uniform integrability proof from Schilling

Published on 09 Apr 2026 - 1:48

score 557 · Answer 11 · 2026-04-12 20:29:25

557

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contraction mapping theorem for 'non-strict' contraction

Published on 12 Apr 2026 - 20:29

score 36 · Answer 12 · 2026-04-12 12:19:11

36

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How to prove sub-additivity of the Lebesgue measure for open sets?

Published on 12 Apr 2026 - 12:19

score 537 · Answer 13 · 2026-04-11 16:11:10

537

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Investigate maxima of Gaussian integral over sphere.

Published on 11 Apr 2026 - 16:11

score 178 · Answer 14 · 2026-04-11 02:07:33

178

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Help with proof that convergence in measure is equivalent to Cauchy convergence in measure if the space is sigma-finite.

Published on 11 Apr 2026 - 2:07

score 27 · Answer 15 · 2026-04-09 21:51:53

27

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Showing function $A \mapsto Ax$ beween normed spaces is bounded

Published on 09 Apr 2026 - 21:51

List Question

Smart tricks used to prove formulas by approximation

Suppose that $f$ has the property that $f(x+y)=f(x)+f(y)$.

The Mean Value Theorem (inequality) for complex-valued functions of several real variables

Showing $h(t):=( s \mapsto\frac{s}{s+2+t})$ is continuous and calculating $\int_{-1}^1h(t)dt$.

If $A\leq \mathbb{Z}$ then $\sup A\in A$

Integral of holomorphic function is again holomorphic

Does a sequence of derivatives takes on its limiting value?

Continuous functions approximating identity

Let $x_n = \sum_{ j=1}^n \frac1j$. Show that for every $k$ we have $\lim _{n→∞} |xn+k −xn| = 0$, yet {$x_n$} is not Cauchy.

Different forms of uniform integrability proof from Schilling

contraction mapping theorem for 'non-strict' contraction

How to prove sub-additivity of the Lebesgue measure for open sets?

Investigate maxima of Gaussian integral over sphere.

Help with proof that convergence in measure is equivalent to Cauchy convergence in measure if the space is sigma-finite.

Showing function $A \mapsto Ax$ beween normed spaces is bounded

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