Question

If $T \colon V \to V$ is a linear operation and $B$ is a basis for $V$, then $T$ is one-to-one $\iff$ $[T]_B$ is invertible.

score 48 · Answer 1 · 2026-04-15 04:22:55

48

Views

If $T \colon V \to V$ is a linear operation and $B$ is a basis for $V$, then $T$ is one-to-one $\iff$ $[T]_B$ is invertible.

Published on 15 Apr 2026 - 4:22

score 54 · Answer 2 · 2026-04-15 20:31:03

54

Views

Proving $f^{-1}(f(x))=x \forall x\in X.$ (if f is bijective).

Published on 15 Apr 2026 - 20:31

score 109 · Answer 3 · 2026-04-16 04:37:58

109

Views

Prove that $(A\setminus B)\cup (B \setminus A)\subseteq (A\cup B)\setminus(A\cap B)$

Published on 16 Apr 2026 - 4:37

score 172 · Answer 4 · 2026-04-13 13:32:13

172

Views

Is this a correct proof of the Pythagorean theorem?

Published on 13 Apr 2026 - 13:32

score 908 · Answer 5 · 2026-04-15 17:54:56

908

Views

Solving $x^2-2x-3<0$

Published on 15 Apr 2026 - 17:54

score 6.8k · Answer 6 · 2026-04-12 01:49:54

6.8k

Views

Prove using vectors two lines bisect each other

Published on 12 Apr 2026 - 1:49

score 103 · Answer 7 · 2026-04-15 00:23:37

103

Views

An infinite $\sigma$-algebra contains a infinite sequence of disjoint nonempty sets, my attempt.

Published on 15 Apr 2026 - 0:23

score 128 · Answer 8 · 2026-04-17 09:09:34

128

Views

the suprema of $p$ norms in a $n$-ball

Published on 17 Apr 2026 - 9:09

score 100 · Answer 9 · 2026-04-14 03:21:19

100

Views

How does one subtract from concatenation in order to prove that $4\times 5 + 67 = 45 + 6\times 7$?

Published on 14 Apr 2026 - 3:21

score 79 · Answer 10 · 2026-04-15 04:40:07

79

Views

Is The Series $\sum_{n=1}^{\infty} \frac{n^4-3n+2}{4n^5+7}$ Divergent

Published on 15 Apr 2026 - 4:40

score 82 · Answer 11 · 2026-04-13 22:37:41

82

Views

Let $K_i$ be a class of structures, show that Th$(\bigcup_{i\in I} K_i)=\bigcap_{i\in I}$Th$(K_i)$

Published on 13 Apr 2026 - 22:37

score 115 · Answer 12 · 2026-04-11 20:19:59

115

Views

Proof explanation: Sufficiency and maximum likelihood

Published on 11 Apr 2026 - 20:19

score 1.4k · Answer 13 · 2026-04-17 02:10:10

1.4k

Views

Very indeterminate form: $\lim_{x \to \infty} \left(\sqrt{x^2+2x+3} -\sqrt{x^2+3}\right)^x \longrightarrow (\infty-\infty)^{\infty}$

Published on 17 Apr 2026 - 2:10

score 705 · Answer 14 · 2026-04-16 03:30:17

705

Views

Find an integer $N$ such that $2^n > n^4$ whenever n is an integer greater than N.

Published on 16 Apr 2026 - 3:30

score 107 · Answer 15 · 2026-04-15 05:13:02

107

Views

Probability Proof $ \mathbb{P}\left(A_{1} \cup A_{2} \cup A_{3}\right) = ... $

Published on 15 Apr 2026 - 5:13

List Question

If $T \colon V \to V$ is a linear operation and $B$ is a basis for $V$, then $T$ is one-to-one $\iff$ $[T]_B$ is invertible.

Proving $f^{-1}(f(x))=x \forall x\in X.$ (if f is bijective).

Prove that $(A\setminus B)\cup (B \setminus A)\subseteq (A\cup B)\setminus(A\cap B)$

Is this a correct proof of the Pythagorean theorem?

Solving $x^2-2x-3<0$

Prove using vectors two lines bisect each other

An infinite $\sigma$-algebra contains a infinite sequence of disjoint nonempty sets, my attempt.

the suprema of $p$ norms in a $n$-ball

How does one subtract from concatenation in order to prove that $4\times 5 + 67 = 45 + 6\times 7$?

Is The Series $\sum_{n=1}^{\infty} \frac{n^4-3n+2}{4n^5+7}$ Divergent

Let $K_i$ be a class of structures, show that Th$(\bigcup_{i\in I} K_i)=\bigcap_{i\in I}$Th$(K_i)$

Proof explanation: Sufficiency and maximum likelihood

Very indeterminate form: $\lim_{x \to \infty} \left(\sqrt{x^2+2x+3} -\sqrt{x^2+3}\right)^x \longrightarrow (\infty-\infty)^{\infty}$

Find an integer $N$ such that $2^n > n^4$ whenever n is an integer greater than N.

Probability Proof $ \mathbb{P}\left(A_{1} \cup A_{2} \cup A_{3}\right) = ... $

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