Question

If $f: \mathbb{R}^n \to \mathbb{R}^n$ is one-to-one, is the differential necessarily one-to-one?

score 78 · Answer 1 · 2018-03-13 11:05:30

78

Views

If $f: \mathbb{R}^n \to \mathbb{R}^n$ is one-to-one, is the differential necessarily one-to-one?

Published on 13 Mar 2018 - 11:05

score 68 · Answer 2 · 2026-03-28 20:51:26

68

Views

Why proof by contradiction here?

Published on 28 Mar 2026 - 20:51

score 232 · Answer 3 · 2026-03-25 21:54:06

232

Views

Quotient of fractional ideals (works as quotient of rational numbers)

Published on 25 Mar 2026 - 21:54

score 150 · Answer 4 · 2018-03-13 16:40:29

150

Views

Use $\epsilon-\delta$ definition to prove that $\lim_{x\rightarrow c}f(x)=L$ if and only if $\lim_{x\rightarrow c}|f(x)-L|=0$

Published on 13 Mar 2018 - 16:40

score 330 · Answer 5 · 2026-03-25 11:16:04

330

Views

Proof verification : $X$ and $Y=g(X)$ are independent random variables $\implies$ $Y$ is degenerate

Published on 25 Mar 2026 - 11:16

score 259 · Answer 6 · 2026-03-28 04:51:16

259

Views

If $T:R^n \to R^m$ is linear, then there is $C>0$ such that $||T(x)|| \leq C||x||$

Published on 28 Mar 2026 - 4:51

score 346 · Answer 7 · 2026-03-25 15:12:15

346

Views

Seeking an example where the Hausdorff distance between two non-empty closed subsets of a metric space is infinite

Published on 25 Mar 2026 - 15:12

score 113 · Answer 8 · 2026-03-27 13:19:31

113

Views

Prove that $\overline{\ln z}=\ln\overline z$

Published on 27 Mar 2026 - 13:19

score 43 · Answer 9 · 2026-03-26 12:04:18

43

Views

Proof for determinants

Published on 26 Mar 2026 - 12:04

score 103 · Answer 10 · 2018-03-13 22:31:05

103

Views

Direct Proof - $ac\leq bc \Rightarrow c \leq 0$

Published on 13 Mar 2018 - 22:31

score 41 · Answer 11 · 2026-03-25 19:01:07

41

Views

Proof Verification/Help: Convergence of sequence

Published on 25 Mar 2026 - 19:01

score 49 · Answer 12 · 2018-03-14 08:26:14

49

Views

Let $f:G\to H$ be a group homomorphism. Let $N \triangleleft H$ be a normal subgroup. Show that $f^{-1}(N)$ is a normal subroup of $G$

Published on 14 Mar 2018 - 8:26

score 87 · Answer 13 · 2018-03-14 08:28:51

87

Views

Derivative of a differentiable continuous function defined on an interval is not necessarily bounded.

Published on 14 Mar 2018 - 8:28

score 332 · Answer 14 · 2026-03-25 06:03:26

332

Views

$L^p$ Banach $ \implies L^2$ Hilbert by Jordan-von Neumann Theorem?

Published on 25 Mar 2026 - 6:03

score 69 · Answer 15 · 2026-03-17 10:23:26

69

Views

The proofs of a variant of Zorn's lemma

Published on 17 Mar 2026 - 10:23

List Question

If $f: \mathbb{R}^n \to \mathbb{R}^n$ is one-to-one, is the differential necessarily one-to-one?

Why proof by contradiction here?

Quotient of fractional ideals (works as quotient of rational numbers)

Use $\epsilon-\delta$ definition to prove that $\lim_{x\rightarrow c}f(x)=L$ if and only if $\lim_{x\rightarrow c}|f(x)-L|=0$

Proof verification : $X$ and $Y=g(X)$ are independent random variables $\implies$ $Y$ is degenerate

If $T:R^n \to R^m$ is linear, then there is $C>0$ such that $||T(x)|| \leq C||x||$

Seeking an example where the Hausdorff distance between two non-empty closed subsets of a metric space is infinite

Prove that $\overline{\ln z}=\ln\overline z$

Proof for determinants

Direct Proof - $ac\leq bc \Rightarrow c \leq 0$

Proof Verification/Help: Convergence of sequence

Let $f:G\to H$ be a group homomorphism. Let $N \triangleleft H$ be a normal subgroup. Show that $f^{-1}(N)$ is a normal subroup of $G$

Derivative of a differentiable continuous function defined on an interval is not necessarily bounded.

$L^p$ Banach $ \implies L^2$ Hilbert by Jordan-von Neumann Theorem?

The proofs of a variant of Zorn's lemma

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