Question

How to prove if $(A \cup B) - (A \cap B) = A$ is true, then $B = \emptyset$?

score 316 · Answer 1 · 2026-04-14 09:05:19

316

Views

How to prove if $(A \cup B) - (A \cap B) = A$ is true, then $B = \emptyset$?

Published on 14 Apr 2026 - 9:05

score 69 · Answer 2 · 2026-04-16 00:29:35

69

Views

If $(S_n)$ converges, then $(\ln \sigma_n )$ converges as well

Published on 16 Apr 2026 - 0:29

score 145 · Answer 3 · 2026-04-15 16:38:30

145

Views

Is the the set of real numbers in the interval $[0,1]$ whose decimal containing only $0$ and $1$ digits countable?

Published on 15 Apr 2026 - 16:38

score 262 · Answer 4 · 2026-04-16 01:20:44

262

Views

Best approximation of a vector $x=\begin{bmatrix}2&2&0&0\end{bmatrix}^\tau$ by the vectors in $M^\perp$, where $b\in M$ is given

Published on 16 Apr 2026 - 1:20

score 602 · Answer 5 · 2026-03-27 07:50:31

602

Views

Measure of an angle "subtended by each pentagon" in a truncated icosahedron

Published on 27 Mar 2026 - 7:50

score 1.4k · Answer 6 · 2026-04-13 10:55:28

1.4k

Views

Why are there multiple base cases in this strong induction?

Published on 13 Apr 2026 - 10:55

score 727 · Answer 7 · 2026-04-14 21:27:11

727

Views

Show that $S = f(f^{-1}(S))$ if and only if $f$ is surjective (used contradiction)

Published on 14 Apr 2026 - 21:27

score 193 · Answer 8 · 2026-04-15 16:29:38

193

Views

Integrability of $\frac{1}{(x^2+y^2+z^2)^a}$ on $E=\{(x,y,z)\in \mathbb{R}^3: z>1, \ z^2(x^2+y^2)<1 \}$

Published on 15 Apr 2026 - 16:29

score 282 · Answer 9 · 2026-04-16 03:55:41

282

Views

Let $f$ be continuous on $X$ and $(x_n)$ be a Cauchy sequence on $X$. Show that $(f(x_n))$ doesnt have to be a Cauchy sequence...

Published on 16 Apr 2026 - 3:55

score 126 · Answer 10 · 2026-04-15 15:30:23

126

Views

Matrix non-singular proof

Published on 15 Apr 2026 - 15:30

score 115 · Answer 11 · 2026-04-14 00:23:29

115

Views

Proof of $\lambda \in \sigma (T)$ implies $|\lambda|\leq ||T||_{B(X)}$

Published on 14 Apr 2026 - 0:23

score 122 · Answer 12 · 2026-03-26 23:09:14

122

Views

Sum $ \sum_{n=0}^{\infty}\frac{n}{n+1}x^{n} $

Published on 26 Mar 2026 - 23:09

score 108 · Answer 13 · 2026-03-25 07:48:01

108

Views

Prove that for an integer $x \ge 7$, it follows that $x\# > x^2+x$

Published on 25 Mar 2026 - 7:48

score 67 · Answer 14 · 2026-04-14 03:40:03

67

Views

If $f_k \rightarrow f$ a.e. on $E$ and $|E|$ is finite, then $f_k \rightarrow f$ in measure on $E$.

Published on 14 Apr 2026 - 3:40

score 199 · Answer 15 · 2026-04-13 00:22:39

199

Views

Basis of annihilator of subspace in $\mathbb{R}^3$

Published on 13 Apr 2026 - 0:22

List Question

How to prove if $(A \cup B) - (A \cap B) = A$ is true, then $B = \emptyset$?

If $(S_n)$ converges, then $(\ln \sigma_n )$ converges as well

Is the the set of real numbers in the interval $[0,1]$ whose decimal containing only $0$ and $1$ digits countable?

Best approximation of a vector $x=\begin{bmatrix}2&2&0&0\end{bmatrix}^\tau$ by the vectors in $M^\perp$, where $b\in M$ is given

Measure of an angle "subtended by each pentagon" in a truncated icosahedron

Why are there multiple base cases in this strong induction?

Show that $S = f(f^{-1}(S))$ if and only if $f$ is surjective (used contradiction)

Integrability of $\frac{1}{(x^2+y^2+z^2)^a}$ on $E=\{(x,y,z)\in \mathbb{R}^3: z>1, \ z^2(x^2+y^2)<1 \}$

Let $f$ be continuous on $X$ and $(x_n)$ be a Cauchy sequence on $X$. Show that $(f(x_n))$ doesnt have to be a Cauchy sequence...

Matrix non-singular proof

Proof of $\lambda \in \sigma (T)$ implies $|\lambda|\leq ||T||_{B(X)}$

Sum $ \sum_{n=0}^{\infty}\frac{n}{n+1}x^{n} $

Prove that for an integer $x \ge 7$, it follows that $x\# > x^2+x$

If $f_k \rightarrow f$ a.e. on $E$ and $|E|$ is finite, then $f_k \rightarrow f$ in measure on $E$.

Basis of annihilator of subspace in $\mathbb{R}^3$

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