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How to use the terms "fixed", "arbitrary", "fixed but arbitrary", "given", "for all" ... in proofs

score 1.1k · Answer 1 · 2026-04-12 03:06:54

1.1k

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How to use the terms "fixed", "arbitrary", "fixed but arbitrary", "given", "for all" ... in proofs

Published on 12 Apr 2026 - 3:06

score 4.6k · Answer 2 · 2026-04-16 18:07:59

4.6k

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gcd(2a+1, 9a+4) = 1

Published on 16 Apr 2026 - 18:07

score 98 · Answer 3 · 2026-04-17 09:03:19

98

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Prove or disprove if $\int_{a}^{b} f$ exists and equals 0

Published on 17 Apr 2026 - 9:03

score 573 · Answer 4 · 2026-04-24 03:51:54

573

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Prove $f[A] \subseteq f[B] \Rightarrow A ⊆ B$, given f is injective.

Published on 24 Apr 2026 - 3:51

score 67 · Answer 5 · 2026-04-16 04:27:53

67

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If $|G|=p^2$, $p$ prime and $G$ is not cyslic $G\cong \Bbb Z/p\Bbb Z\times \Bbb Z/p\Bbb Z $

Published on 16 Apr 2026 - 4:27

score 79 · Answer 6 · 2026-04-14 13:45:37

79

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Verification for $\int_{-\infty}^\infty \frac{\cos(az)}{z^{2n}+1}dz$

Published on 14 Apr 2026 - 13:45

score 585 · Answer 7 · 2026-04-10 21:22:50

585

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Proof of a.s. uniqueness of probability convergence limit

Published on 10 Apr 2026 - 21:22

score 78 · Answer 8 · 2026-04-12 03:23:27

78

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Is my approach correct to this equation?

Published on 12 Apr 2026 - 3:23

score 66 · Answer 9 · 2026-04-17 12:26:31

66

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Find $m \in \mathbb C$ such that $ f(p) = p'(t-m)-p(1)(t+m)^2 + p(0)t^2 $ is isomorphism

Published on 17 Apr 2026 - 12:26

score 45 · Answer 10 · 2026-04-12 08:34:52

45

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Proof regarding the genus of a topological space

Published on 12 Apr 2026 - 8:34

score 120 · Answer 11 · 2026-04-12 22:07:52

120

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Does a bounded function $f$ on $\mathbb R$ has zero for its second derivative?

Published on 12 Apr 2026 - 22:07

score 59 · Answer 12 · 2026-04-16 18:54:58

59

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Proving $\int_{a}^{b}( f+g) = \int_{a}^{b} f + \int_{a}^{b} g$

Published on 16 Apr 2026 - 18:54

score 183 · Answer 13 · 2026-04-17 15:11:37

183

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Find an Example for a linear map $T: \mathbb{F}^4 \to \mathbb{F}^4$ such that $ImT = KerT = sp\{(1, 1, 1, 1), (1, 1, 1, 0)\}$

Published on 17 Apr 2026 - 15:11

score 68 · Answer 14 · 2026-04-15 05:28:21

68

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Is there is an entire function $f$ such that $f(1)=\pi$ and $f'(z)=|z|f(z)$ for all $z\in\mathbb C$?

Published on 15 Apr 2026 - 5:28

score 57 · Answer 15 · 2026-04-12 18:40:58

57

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if $f$ is linear transformation, is proof that $f(U)$ is linear subspace and find its dim

Published on 12 Apr 2026 - 18:40

List Question

How to use the terms "fixed", "arbitrary", "fixed but arbitrary", "given", "for all" ... in proofs

gcd(2a+1, 9a+4) = 1

Prove or disprove if $\int_{a}^{b} f$ exists and equals 0

Prove $f[A] \subseteq f[B] \Rightarrow A ⊆ B$, given f is injective.

If $|G|=p^2$, $p$ prime and $G$ is not cyslic $G\cong \Bbb Z/p\Bbb Z\times \Bbb Z/p\Bbb Z $

Verification for $\int_{-\infty}^\infty \frac{\cos(az)}{z^{2n}+1}dz$

Proof of a.s. uniqueness of probability convergence limit

Is my approach correct to this equation?

Find $m \in \mathbb C$ such that $ f(p) = p'(t-m)-p(1)(t+m)^2 + p(0)t^2 $ is isomorphism

Proof regarding the genus of a topological space

Does a bounded function $f$ on $\mathbb R$ has zero for its second derivative?

Proving $\int_{a}^{b}( f+g) = \int_{a}^{b} f + \int_{a}^{b} g$

Find an Example for a linear map $T: \mathbb{F}^4 \to \mathbb{F}^4$ such that $ImT = KerT = sp\{(1, 1, 1, 1), (1, 1, 1, 0)\}$

Is there is an entire function $f$ such that $f(1)=\pi$ and $f'(z)=|z|f(z)$ for all $z\in\mathbb C$?

if $f$ is linear transformation, is proof that $f(U)$ is linear subspace and find its dim

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