Question

Two nested proofs by induction: one inside the other (and co-dependent)

score 99 · Answer 1 · 2026-04-17 08:27:58

99

Views

Two nested proofs by induction: one inside the other (and co-dependent)

Published on 17 Apr 2026 - 8:27

score 597 · Answer 2 · 2026-04-11 18:48:05

597

Views

Product measure space generated by two sigma finite measure spaces

Published on 11 Apr 2026 - 18:48

score 99 · Answer 3 · 2026-04-11 15:56:08

99

Views

How can I express $(1+2+\dots+(k+1))^2$ using a $\sum$ instead?

Published on 11 Apr 2026 - 15:56

score 948 · Answer 4 · 2026-04-17 11:06:33

948

Views

Show that if $|G|=30$ then $G$ has normal $3$-Sylow and $5$-Sylow

Published on 17 Apr 2026 - 11:06

score 292 · Answer 5 · 2026-04-15 04:39:50

292

Views

Prove that for any family of sets $\mathcal F$, $\bigcup!\mathcal F=\bigcup\mathcal F$ iff $\mathcal F$ is pairwise disjoint.

Published on 15 Apr 2026 - 4:39

score 58 · Answer 6 · 2026-04-16 06:30:35

58

Views

Let $\mathcal{F} = \left\{\bigcup_{i\in J}A_{i}:J\subset\mathbb{N}\right\}$. Show that $\mathcal{F}$ is a $\sigma$-algebra.

Published on 16 Apr 2026 - 6:30

score 247 · Answer 7 · 2026-04-15 13:20:51

247

Views

Show that $\mathcal{F}$ is an algebra but not a $\sigma$-algebra.

Published on 15 Apr 2026 - 13:20

score 49 · Answer 8 · 2026-04-14 12:17:33

49

Views

Verify that $\mathcal{A}$ is a $\pi$-system and also determine $\lambda\langle\mathcal{A}\rangle$, the $\lambda$-system generated by $\mathcal{A}$.

Published on 14 Apr 2026 - 12:17

score 140 · Answer 9 · 2026-04-16 15:21:22

Let $f$ be an entire. Show that, if $f(z_n) \to \infty$ for all sequences $z_n$ such that $z_n \to \infty$, then f must be a polynomial.

score 51 · Answer 10 · 2026-04-15 15:11:49

51

Views

Prove that montonicity and continuity imply bijectivity.

Published on 15 Apr 2026 - 15:11

score 27 · Answer 11 · 2026-04-23 02:19:05

27

Views

Evaluate the induced measure $mT^{-1}(A)$ of the set $A$ in the following cases.

Published on 23 Apr 2026 - 2:19

score 44 · Answer 12 · 2026-04-10 23:45:05

44

Views

How to correctly argue that this function preserves the norm?

Published on 10 Apr 2026 - 23:45

score 173 · Answer 13 · 2026-04-13 21:27:17

173

Views

The set of elements of order $7$ of $A_7$ is not a conjugacy class.

Published on 13 Apr 2026 - 21:27

score 3.8k · Answer 14 · 2026-04-11 09:07:13

3.8k

Views

Probability of getting off the bus in drinking game "Ride the Bus"

Published on 11 Apr 2026 - 9:07

score 106 · Answer 15 · 2026-04-15 04:02:19

106

Views

If $n > 1$, there are no non-zero $*$-homomorphisms $M_n(\Bbb{C}) \to \Bbb{C}$

Published on 15 Apr 2026 - 4:02

List Question

Two nested proofs by induction: one inside the other (and co-dependent)

Product measure space generated by two sigma finite measure spaces

How can I express $(1+2+\dots+(k+1))^2$ using a $\sum$ instead?

Show that if $|G|=30$ then $G$ has normal $3$-Sylow and $5$-Sylow

Prove that for any family of sets $\mathcal F$, $\bigcup!\mathcal F=\bigcup\mathcal F$ iff $\mathcal F$ is pairwise disjoint.

Let $\mathcal{F} = \left\{\bigcup_{i\in J}A_{i}:J\subset\mathbb{N}\right\}$. Show that $\mathcal{F}$ is a $\sigma$-algebra.

Show that $\mathcal{F}$ is an algebra but not a $\sigma$-algebra.

Verify that $\mathcal{A}$ is a $\pi$-system and also determine $\lambda\langle\mathcal{A}\rangle$, the $\lambda$-system generated by $\mathcal{A}$.

Let $f$ be an entire. Show that, if $f(z_n) \to \infty$ for all sequences $z_n$ such that $z_n \to \infty$, then f must be a polynomial.

Prove that montonicity and continuity imply bijectivity.

Evaluate the induced measure $mT^{-1}(A)$ of the set $A$ in the following cases.

How to correctly argue that this function preserves the norm?

The set of elements of order $7$ of $A_7$ is not a conjugacy class.

Probability of getting off the bus in drinking game "Ride the Bus"

If $n > 1$, there are no non-zero $*$-homomorphisms $M_n(\Bbb{C}) \to \Bbb{C}$

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