Question

Within If and Only If Proofs, why can the proof for one direction be easier than the other?

score 1k · Answer 1 · 2026-04-14 04:11:27

1k

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Within If and Only If Proofs, why can the proof for one direction be easier than the other?

Published on 14 Apr 2026 - 4:11

score 1.7k · Answer 2 · 2026-04-13 23:37:39

1.7k

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When does one proof of one direction of an If and Only If proof suffice?

Published on 13 Apr 2026 - 23:37

score 310 · Answer 3 · 2026-04-14 06:29:30

310

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Proof. sup{ f(x) } - inf{ f(x) } $\ge$ sup{ |f(x)| } - inf{ |f(x)| } (Abbott pp 198 q7.4.1)

Published on 14 Apr 2026 - 6:29

score 2.3k · Answer 4 · 2026-04-08 02:28:00

2.3k

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Differential forms turn infinitesimal stuff rigorous?

Published on 08 Apr 2026 - 2:28

score 195 · Answer 5 · 2026-03-28 13:04:35

195

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If $\int^{b}_a f > 0$ then there is some interval and $\delta > 0$ on which $f(x) \ge \delta$ (Abbott pp 199 q7.4.4d)

Published on 28 Mar 2026 - 13:04

score 215 · Answer 6 · 2014-03-07 08:29:00

215

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If $g \ge 0$ is continuous on $[a,b]$ and $g(x_0) > 0$ then $\int^{b}_a g > 0$ (Abbott pp 199 q7.4.4c)

Published on 07 Mar 2014 - 8:29

score 2.6k · Answer 7 · 2026-04-12 08:31:17

2.6k

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How would one arrive at the formulas for divergence and curl?

Published on 12 Apr 2026 - 8:31

score 374 · Answer 8 · 2026-04-13 22:37:49

374

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Geometry of $k$-forms and $k$-vectors

Published on 13 Apr 2026 - 22:37

score 436 · Answer 9 · 2026-04-09 19:54:45

436

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Intuition and counterexamples for higher-order derivative test

Published on 09 Apr 2026 - 19:54

score 544 · Answer 10 · 2026-04-14 03:30:38

How to presage Prove by Contrapositive, for Sequential Characterizations of Limit and Continuity? (Abbott pp 106 t4.2.3, 110 t4.3.2)

score 3.5k · Answer 11 · 2026-04-11 14:31:02

3.5k

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Why are we interested in irreducible representation but not faithful representation?

Published on 11 Apr 2026 - 14:31

score 21 · Answer 12 · 2026-03-25 15:22:44

21

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When is a series expansion related to its derivative by a polynomial equation?

Published on 25 Mar 2026 - 15:22

score 1.1k · Answer 13 · 2026-04-13 02:52:54

1.1k

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Derivative of exponential functions

Published on 13 Apr 2026 - 2:52

score 1.1k · Answer 14 · 2026-04-01 00:09:30

1.1k

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Why do statisticians like "$n-1$" instead of "$n$"?

Published on 01 Apr 2026 - 0:09

score 177 · Answer 15 · 2026-04-13 22:58:49

177

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Soft question: How can I make sure that I understand material without any practice problems?

Published on 13 Apr 2026 - 22:58

List Question

Within If and Only If Proofs, why can the proof for one direction be easier than the other?

When does one proof of one direction of an If and Only If proof suffice?

Proof. sup{ f(x) } - inf{ f(x) } $\ge$ sup{ |f(x)| } - inf{ |f(x)| } (Abbott pp 198 q7.4.1)

Differential forms turn infinitesimal stuff rigorous?

If $\int^{b}_a f > 0$ then there is some interval and $\delta > 0$ on which $f(x) \ge \delta$ (Abbott pp 199 q7.4.4d)

If $g \ge 0$ is continuous on $[a,b]$ and $g(x_0) > 0$ then $\int^{b}_a g > 0$ (Abbott pp 199 q7.4.4c)

How would one arrive at the formulas for divergence and curl?

Geometry of $k$-forms and $k$-vectors

Intuition and counterexamples for higher-order derivative test

How to presage Prove by Contrapositive, for Sequential Characterizations of Limit and Continuity? (Abbott pp 106 t4.2.3, 110 t4.3.2)

Why are we interested in irreducible representation but not faithful representation?

When is a series expansion related to its derivative by a polynomial equation?

Derivative of exponential functions

Why do statisticians like "$n-1$" instead of "$n$"?

Soft question: How can I make sure that I understand material without any practice problems?

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