Question

What's the logic of this statement? "Define $xCy$ if $x^2<y^2$, or if $x^2 = y^2$ and $x<y$."

score 58 · Answer 1 · 2026-03-25 15:12:12

58

Views

What's the logic of this statement? "Define $xCy$ if $x^2<y^2$, or if $x^2 = y^2$ and $x<y$."

Published on 25 Mar 2026 - 15:12

score 68 · Answer 2 · 2018-02-07 04:21:06

68

Views

Showing that $f(x) = f(0) + \int_0^xf'(t)dt = f(0) + f'(0)x + \int_0^x(x-t)f''(t)dt$ through integration by parts

Published on 07 Feb 2018 - 4:21

score 416 · Answer 3 · 2026-04-10 18:50:29

416

Views

How obvious must it be before being allowed to use "Without Loss of Generality" in a proof

Published on 10 Apr 2026 - 18:50

score 251 · Answer 4 · 2026-03-26 07:33:19

251

Views

Let $(X,d_{disc})$. Show that $E\subset X$ is disconnected

Published on 26 Mar 2026 - 7:33

score 465 · Answer 5 · 2026-04-09 01:53:15

465

Views

Deductive Logic Proof

Published on 09 Apr 2026 - 1:53

score 74 · Answer 6 · 2026-03-25 03:04:16

74

Views

Prove using the rule of inference: ∀x (L(x)→ F(x)) and ∃x (L(x) ∧ ¬C(x)) imply ∃x(F(x) ∧ ¬C(x))

Published on 25 Mar 2026 - 3:04

score 58 · Answer 7 · 2026-04-09 00:09:09

58

Views

Mistake in the wording of a question about the cardinality of a set of primes?

Published on 09 Apr 2026 - 0:09

score 70 · Answer 8 · 2026-03-26 07:37:38

70

Views

Proving a floor function

Published on 26 Mar 2026 - 7:37

score 1.5k · Answer 9 · 2026-03-25 10:25:33

1.5k

Views

$s + \frac{1}{n}$ is an upper bound for $A$ and $s - \frac{1}{n}$ is not an upper bound for $A$. Show $s = \sup A.$

Published on 25 Mar 2026 - 10:25

score 39 · Answer 10 · 2026-04-08 08:51:43

39

Views

Does this method of proof work?

Published on 08 Apr 2026 - 8:51

score 46 · Answer 11 · 2018-02-08 02:38:47

46

Views

Is $f:\mathbb{R}^2 \rightarrow \mathbb{R}^2 ,f(x,y)=(x+4y,-3x-12y)$ surjective?

Published on 08 Feb 2018 - 2:38

score 221 · Answer 12 · 2026-03-25 17:17:18

221

Views

Discrete Valuation Ring properties

Published on 25 Mar 2026 - 17:17

score 2.4k · Answer 13 · 2026-03-25 06:29:06

2.4k

Views

Proof: If a ≡ b (mod n) then am ≡ bm (mod mn) and converse

Published on 25 Mar 2026 - 6:29

score 53 · Answer 14 · 2026-04-09 03:39:16

53

Views

critique on the style and layout of my proof

Published on 09 Apr 2026 - 3:39

score 31 · Answer 15 · 2026-04-10 03:23:43

31

Views

Width at half the maximum height of a sin-function is one-third of wavelength?

Published on 10 Apr 2026 - 3:23

List Question

What's the logic of this statement? "Define $xCy$ if $x^2<y^2$, or if $x^2 = y^2$ and $x<y$."

Showing that $f(x) = f(0) + \int_0^xf'(t)dt = f(0) + f'(0)x + \int_0^x(x-t)f''(t)dt$ through integration by parts

How obvious must it be before being allowed to use "Without Loss of Generality" in a proof

Let $(X,d_{disc})$. Show that $E\subset X$ is disconnected

Deductive Logic Proof

Prove using the rule of inference: ∀x (L(x)→ F(x)) and ∃x (L(x) ∧ ¬C(x)) imply ∃x(F(x) ∧ ¬C(x))

Mistake in the wording of a question about the cardinality of a set of primes?

Proving a floor function

$s + \frac{1}{n}$ is an upper bound for $A$ and $s - \frac{1}{n}$ is not an upper bound for $A$. Show $s = \sup A.$

Does this method of proof work?

Is $f:\mathbb{R}^2 \rightarrow \mathbb{R}^2 ,f(x,y)=(x+4y,-3x-12y)$ surjective?

Discrete Valuation Ring properties

Proof: If a ≡ b (mod n) then am ≡ bm (mod mn) and converse

critique on the style and layout of my proof

Width at half the maximum height of a sin-function is one-third of wavelength?

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