Question

Functions and sets. Show that if A is a subset of X, then $f^{-1}(f(A))\supseteq A$. Find an example where $f^{-1}(f(A))\neq A$.

score 46 · Answer 1 · 2026-04-15 08:39:35

46

Views

Functions and sets. Show that if A is a subset of X, then $f^{-1}(f(A))\supseteq A$. Find an example where $f^{-1}(f(A))\neq A$.

Published on 15 Apr 2026 - 8:39

score 190 · Answer 2 · 2026-04-22 20:32:28

190

Views

Proving Szemerédi's Theorem using the Simplex Removal Lemma for $k$-Uniform Hypergraphs.

Published on 22 Apr 2026 - 20:32

score 24 · Answer 3 · 2026-04-14 05:52:04

24

Views

Minimum 1-D finite pavement to fit in varying-length K bricks

Published on 14 Apr 2026 - 5:52

score 359 · Answer 4 · 2026-04-14 17:11:04

359

Views

Find the bounds of the number of leaves in a tree

Published on 14 Apr 2026 - 17:11

score 57 · Answer 5 · 2026-04-15 12:28:03

57

Views

Is it true that $\sum_{k=0}^{n}k\cdot \left(\begin{array}{l}{n}\\{k}\end{array}\right)=O\left(2 ^ {n\log _{3}n}\right)?$

Published on 15 Apr 2026 - 12:28

score 772 · Answer 6 · 2026-04-17 19:07:16

772

Views

Find the number of trees on $2m$ given vertices in which all vertices have degree $1$ or $3$.

Published on 17 Apr 2026 - 19:07

score 144 · Answer 7 · 2026-04-14 17:45:18

144

Views

Linear order on the set N^N

Published on 14 Apr 2026 - 17:45

score 247 · Answer 8 · 2026-04-12 20:40:45

247

Views

How to compute the syndrome polynomial? BCH code

Published on 12 Apr 2026 - 20:40

score 32 · Answer 9 · 2026-04-11 22:08:17

32

Views

Density of linear order where $|A| = 1$

Published on 11 Apr 2026 - 22:08

score 245 · Answer 10 · 2026-04-22 16:37:06

245

Views

Lucas number identity

Published on 22 Apr 2026 - 16:37

score 79 · Answer 11 · 2026-04-17 08:21:53

79

Views

Given a graph $G = (V, E),$ prove that if $|E| > \binom{ |V| -1}{2}$ then the graph is connected.

Published on 17 Apr 2026 - 8:21

score 116 · Answer 12 · 2026-04-16 01:17:13

116

Views

Prove $p \lor q \Leftrightarrow (\neg p) \rightarrow q$, but with caveats.

Published on 16 Apr 2026 - 1:17

score 2.6k · Answer 13 · 2026-04-12 05:47:11

2.6k

Views

Given a relation $R$, what is the $R^{-1}$, and what is the complement of $R$ on $A$?

Published on 12 Apr 2026 - 5:47

score 73 · Answer 14 · 2026-04-11 18:27:34

73

Views

Consider $X$ a countably infinite set, is $\{X \cup x\}$ with $x \notin X$ countably infinite?

Published on 11 Apr 2026 - 18:27

score 227 · Answer 15 · 2026-04-16 13:06:13

227

Views

Prove by induction: For $n\in{\Bbb N}$ and $n\geq{12}$ there are $a,b\in\Bbb{N}$ such that: $n=4a+5b$.

Published on 16 Apr 2026 - 13:06

List Question

Functions and sets. Show that if A is a subset of X, then $f^{-1}(f(A))\supseteq A$. Find an example where $f^{-1}(f(A))\neq A$.

Proving Szemerédi's Theorem using the Simplex Removal Lemma for $k$-Uniform Hypergraphs.

Minimum 1-D finite pavement to fit in varying-length K bricks

Find the bounds of the number of leaves in a tree

Is it true that $\sum_{k=0}^{n}k\cdot \left(\begin{array}{l}{n}\\{k}\end{array}\right)=O\left(2 ^ {n\log _{3}n}\right)?$

Find the number of trees on $2m$ given vertices in which all vertices have degree $1$ or $3$.

Linear order on the set N^N

How to compute the syndrome polynomial? BCH code

Density of linear order where $|A| = 1$

Lucas number identity

Given a graph $G = (V, E),$ prove that if $|E| > \binom{ |V| -1}{2}$ then the graph is connected.

Prove $p \lor q \Leftrightarrow (\neg p) \rightarrow q$, but with caveats.

Given a relation $R$, what is the $R^{-1}$, and what is the complement of $R$ on $A$?

Consider $X$ a countably infinite set, is $\{X \cup x\}$ with $x \notin X$ countably infinite?

Prove by induction: For $n\in{\Bbb N}$ and $n\geq{12}$ there are $a,b\in\Bbb{N}$ such that: $n=4a+5b$.

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