Question

Proof of if $U,W$ are finite subspaces of $V$, then $dim(U \oplus W)\leq dim(V)$

score 55 · Answer 1 · 2023-02-11 19:32:18

55

Views

Proof of if $U,W$ are finite subspaces of $V$, then $dim(U \oplus W)\leq dim(V)$

Published on 11 Feb 2023 - 19:32

score 46 · Answer 2 · 2023-02-11 19:32:49

46

Views

May the proof of Calculus on Manifolds Theorem 3-11 (on compact sets) be simplified as follows?

Published on 11 Feb 2023 - 19:32

score 44 · Answer 3 · 2023-02-12 12:57:14

44

Views

Logic solution check to solving system of quadratic equations exercise. Also interested in alternative solutions that are algebraic only.

Published on 12 Feb 2023 - 12:57

score 200 · Answer 4 · 2023-02-12 22:18:20

200

Views

Alternative proofs of “length of linearly independent list is less than or equal to length of spanning list”

Published on 12 Feb 2023 - 22:18

score 202 · Answer 5 · 2026-03-26 08:00:52

202

Views

Can Lawson's proof (that the canonical inclusion into a Clifford algebra is injective) be fixed?

Published on 26 Mar 2026 - 8:00

score 163 · Answer 6 · 2023-02-13 14:54:12

163

Views

More elegant way to prove $\cos(\phi)\leq 1-\frac{2\phi^2}{\pi^2} $?

Published on 13 Feb 2023 - 14:54

score 129 · Answer 7 · 2026-04-04 16:52:57

129

Views

Is there a proof $e^ae^b=e^{a+b}$ using its power series expansion?

Published on 04 Apr 2026 - 16:52

score 37 · Answer 8 · 2023-02-17 05:40:57

37

Views

Can we use closeness results to show surjectivity?

Published on 17 Feb 2023 - 5:40

score 74 · Answer 9 · 2023-02-19 15:04:20

74

Views

Metric in terms of curvature (proof verification)

Published on 19 Feb 2023 - 15:04

score 86 · Answer 10 · 2026-03-27 03:59:12

86

Views

Alternative (intuitive) proof of change of variables for integration(Jacobian)

Published on 27 Mar 2026 - 3:59

score 114 · Answer 11 · 2023-02-20 23:55:34

114

Views

Alternative ways of showing that $x^2 + 1$ is prime in $\mathbb{Z}[x]$.

Published on 20 Feb 2023 - 23:55

score 302 · Answer 12 · 2026-03-26 04:53:48

302

Views

Prove that $|(a,b)\cup (c,d)|=(b-a)+(d-c)\text{ if and only if }(a,b)\cap (c,d)=\emptyset.$ ("Measure, Integration & Real Analysis" by Sheldon Axler)

Published on 26 Mar 2026 - 4:53

score 134 · Answer 13 · 2023-02-24 05:11:09

134

Views

A finitely generated group $G$ is divisible group iff trivial.

Published on 24 Feb 2023 - 5:11

score 106 · Answer 14 · 2023-02-25 13:14:00

106

Views

Find $|f(-1)|$ where $f(x)=\int\frac{x^7+2}{(x^2+x+1)^2}dx$

Published on 25 Feb 2023 - 13:14

score 112 · Answer 15 · 2026-03-31 21:09:40

112

Views

Formula for the tangent to an ellipse at a given point (splitting formula)

Published on 31 Mar 2026 - 21:09

List Question

Proof of if $U,W$ are finite subspaces of $V$, then $dim(U \oplus W)\leq dim(V)$

May the proof of Calculus on Manifolds Theorem 3-11 (on compact sets) be simplified as follows?

Logic solution check to solving system of quadratic equations exercise. Also interested in alternative solutions that are algebraic only.

Alternative proofs of “length of linearly independent list is less than or equal to length of spanning list”

Can Lawson's proof (that the canonical inclusion into a Clifford algebra is injective) be fixed?

More elegant way to prove $\cos(\phi)\leq 1-\frac{2\phi^2}{\pi^2} $?

Is there a proof $e^ae^b=e^{a+b}$ using its power series expansion?

Can we use closeness results to show surjectivity?

Metric in terms of curvature (proof verification)

Alternative (intuitive) proof of change of variables for integration(Jacobian)

Alternative ways of showing that $x^2 + 1$ is prime in $\mathbb{Z}[x]$.

Prove that $|(a,b)\cup (c,d)|=(b-a)+(d-c)\text{ if and only if }(a,b)\cap (c,d)=\emptyset.$ ("Measure, Integration & Real Analysis" by Sheldon Axler)

A finitely generated group $G$ is divisible group iff trivial.

Find $|f(-1)|$ where $f(x)=\int\frac{x^7+2}{(x^2+x+1)^2}dx$

Formula for the tangent to an ellipse at a given point (splitting formula)

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