Question

How can I prove this proposition from Peano Axioms: (Cancellation law). Let a, b, c be natural numbers such that a + b = a + c. Then we have b = c.

score 757 · Answer 1 · 2026-04-16 03:09:32

757

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How can I prove this proposition from Peano Axioms: (Cancellation law). Let a, b, c be natural numbers such that a + b = a + c. Then we have b = c.

Published on 16 Apr 2026 - 3:09

score 34 · Answer 2 · 2026-04-10 09:39:57

34

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How to build sinewave sweep from constant frequency & amplitude sinewaves

Published on 10 Apr 2026 - 9:39

score 80 · Answer 3 · 2026-04-14 23:14:46

80

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Calculating the symbolic solution to a definite integral containing trigonometric functions

Published on 14 Apr 2026 - 23:14

score 100 · Answer 4 · 2026-04-16 22:45:14

100

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Prove that $x\,\int_a^x\,\frac{1}{s^2}\,\int_a^s\,t\,f(t)\,\text{d}t\,\text{d}s - \int_a^x\,\int_a^s\,f(t)\,\text{d}t\,\text{d}s$ is linear in $x$.

Published on 16 Apr 2026 - 22:45

score 269 · Answer 5 · 2026-04-10 06:20:18

269

Views

Quotient topology and continuity

Published on 10 Apr 2026 - 6:20

score 328 · Answer 6 · 2026-03-25 07:48:29

328

Views

How to check for local extrema or saddle point given an semidefinite matrix

Published on 25 Mar 2026 - 7:48

score 1k · Answer 7 · 2026-04-15 05:58:08

1k

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Examples of the Carathéodory extension theorem

Published on 15 Apr 2026 - 5:58

score 64 · Answer 8 · 2026-04-16 14:31:45

64

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$\int_{-1}^0 \sin^{2} (\frac{\pi}{2} f(x+1)) dx +\int_{0}^1 \cos^{2} (\frac{\pi}{2} f(x)) dx =?$

Published on 16 Apr 2026 - 14:31

score 227 · Answer 9 · 2026-04-15 20:31:25

227

Views

For every continuous function $g$ does there exists a sequence of functions $\{f_n\}$ which converges to $g$?

Published on 15 Apr 2026 - 20:31

score 621 · Answer 10 · 2026-04-15 23:54:13

621

Views

Lissajous Curve dense in a Volume

Published on 15 Apr 2026 - 23:54

score 351 · Answer 11 · 2026-04-16 02:27:12

351

Views

Prob. 12, Sec. 4.2, in Bartle & Sherbert's INTRO TO REAL ANALYSIS: If $f(x+y)=f(x)+f(y)$ for all $x, y$ and if $\lim_{x\to 0} f(x)$ exists, . . .

Published on 16 Apr 2026 - 2:27

score 153 · Answer 12 · 2026-04-15 23:14:17

153

Views

Prob. 15, Sec. 4.2, in Bartle & Sherbert's INTRO TO REAL ANALYSIS: $\lim_{x\to c}\sqrt{f(x)}=\sqrt{\lim_{x\to c}f(x)}$

Published on 15 Apr 2026 - 23:14

score 113 · Answer 13 · 2026-04-09 08:06:57

113

Views

Studying the total variation of an Integral Function

Published on 09 Apr 2026 - 8:06

score 100 · Answer 14 · 2026-04-17 12:07:08

100

Views

Name for this condition: $\forall\epsilon > 0:\quad P(\exists m\ge n: |X_m - X|>\epsilon)\to 0,\quad n\to\infty$

Published on 17 Apr 2026 - 12:07

score 97 · Answer 15 · 2026-04-14 09:50:11

97

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Continuity of an exponential series

Published on 14 Apr 2026 - 9:50

List Question

How can I prove this proposition from Peano Axioms: (Cancellation law). Let a, b, c be natural numbers such that a + b = a + c. Then we have b = c.

How to build sinewave sweep from constant frequency & amplitude sinewaves

Calculating the symbolic solution to a definite integral containing trigonometric functions

Prove that $x\,\int_a^x\,\frac{1}{s^2}\,\int_a^s\,t\,f(t)\,\text{d}t\,\text{d}s - \int_a^x\,\int_a^s\,f(t)\,\text{d}t\,\text{d}s$ is linear in $x$.

Quotient topology and continuity

How to check for local extrema or saddle point given an semidefinite matrix

Examples of the Carathéodory extension theorem

$\int_{-1}^0 \sin^{2} (\frac{\pi}{2} f(x+1)) dx +\int_{0}^1 \cos^{2} (\frac{\pi}{2} f(x)) dx =?$

For every continuous function $g$ does there exists a sequence of functions $\{f_n\}$ which converges to $g$?

Lissajous Curve dense in a Volume

Prob. 12, Sec. 4.2, in Bartle & Sherbert's INTRO TO REAL ANALYSIS: If $f(x+y)=f(x)+f(y)$ for all $x, y$ and if $\lim_{x\to 0} f(x)$ exists, . . .

Prob. 15, Sec. 4.2, in Bartle & Sherbert's INTRO TO REAL ANALYSIS: $\lim_{x\to c}\sqrt{f(x)}=\sqrt{\lim_{x\to c}f(x)}$

Studying the total variation of an Integral Function

Name for this condition: $\forall\epsilon > 0:\quad P(\exists m\ge n: |X_m - X|>\epsilon)\to 0,\quad n\to\infty$

Continuity of an exponential series

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