Question

Kunze & Hoffman Linear algebra, equivalenece of two homogeneous systems proof verification request

score 114 · Answer 1 · 2020-04-14 12:56:22

114

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Kunze & Hoffman Linear algebra, equivalenece of two homogeneous systems proof verification request

Published on 14 Apr 2020 - 12:56

score 182 · Answer 2 · 2020-04-14 13:59:18

182

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Is $\{ \sin(\sqrt {nx} \mid n\in \mathbb N\}$ is equicontinuous in $C[0,1]$?

Published on 14 Apr 2020 - 13:59

score 392 · Answer 3 · 2020-04-14 14:58:34

392

Views

Proof verification $\lim_{x \rightarrow 0}{\sin(\frac{\pi}{x})}$ does not exist.

Published on 14 Apr 2020 - 14:58

score 149 · Answer 4 · 2026-03-27 00:55:08

149

Views

Doubt in IMO 1982 problem 1

Published on 27 Mar 2026 - 0:55

score 3k · Answer 5 · 2026-03-25 17:52:09

3k

Views

Suppose that $\mathcal{B}$ is a basis for $V$. Prove that $T$ is an isomorphism if and only if $T(\mathcal{B})$ is a basis for $W$.

Published on 25 Mar 2026 - 17:52

score 203 · Answer 6 · 2020-04-14 20:39:34

203

Views

Prove that the fast exponentiation algorithm halts after $\lceil \log_2n \rceil+1$ steps

Published on 14 Apr 2020 - 20:39

score 615 · Answer 7 · 2026-04-04 13:43:27

615

Views

Is every cubic extension of $\mathbb{Q}$ of the form $\mathbb{Q}(\sqrt[3]{d})$ for some $d \in \mathbb{Q}$?

Published on 04 Apr 2026 - 13:43

score 32 · Answer 8 · 2026-04-08 17:25:43

32

Views

Diferentiating an equation

Published on 08 Apr 2026 - 17:25

score 341 · Answer 9 · 2020-04-15 00:52:43

341

Views

Showing uniqueness property over a vector space that is the direct sum of two of its subspaces.

Published on 15 Apr 2020 - 0:52

score 223 · Answer 10 · 2020-04-15 01:21:44

223

Views

Basic real analysis proof: every real number has a unique integer part

Published on 15 Apr 2020 - 1:21

score 53 · Answer 11 · 2020-04-15 01:22:28

53

Views

Let $(a_n)_{n=0}^\infty$ be bounded and $(b_n)_{n=0}^\infty$ be equivalent to $(a_n)_{n=0}^\infty$. Show $(b_n)_{n=0}^\infty$ is bounded.

Published on 15 Apr 2020 - 1:22

score 89 · Answer 12 · 2020-04-15 02:52:34

89

Views

Prove that whenever $n$ and $m$ are natural numbers such that $m > n$, then we have $a_{m} > a_{n}$

Published on 15 Apr 2020 - 2:52

score 67 · Answer 13 · 2026-02-23 02:50:27

67

Views

Suppose that $(a_{n})_{n=m}^{\infty}$ is a convergent sequence of real numbers. Then $(a_{n})_{n=m}^{\infty}$ is also a Cauchy sequence.

Published on 23 Feb 2026 - 2:50

score 1.9k · Answer 14 · 2020-04-15 04:40:08

1.9k

Views

What is the number of all compositions of $n$ in which the first part is not $2$?

Published on 15 Apr 2020 - 4:40

score 144 · Answer 15 · 2026-03-28 02:23:28

144

Views

Derive Likelihood Ratio test for testing $H_0: \mu=\sigma^2$, $H_1: \mu \not= \sigma^2$.

Published on 28 Mar 2026 - 2:23

List Question

Kunze & Hoffman Linear algebra, equivalenece of two homogeneous systems proof verification request

Is $\{ \sin(\sqrt {nx} \mid n\in \mathbb N\}$ is equicontinuous in $C[0,1]$?

Proof verification $\lim_{x \rightarrow 0}{\sin(\frac{\pi}{x})}$ does not exist.

Doubt in IMO 1982 problem 1

Suppose that $\mathcal{B}$ is a basis for $V$. Prove that $T$ is an isomorphism if and only if $T(\mathcal{B})$ is a basis for $W$.

Prove that the fast exponentiation algorithm halts after $\lceil \log_2n \rceil+1$ steps

Is every cubic extension of $\mathbb{Q}$ of the form $\mathbb{Q}(\sqrt[3]{d})$ for some $d \in \mathbb{Q}$?

Diferentiating an equation

Showing uniqueness property over a vector space that is the direct sum of two of its subspaces.

Basic real analysis proof: every real number has a unique integer part

Let $(a_n)_{n=0}^\infty$ be bounded and $(b_n)_{n=0}^\infty$ be equivalent to $(a_n)_{n=0}^\infty$. Show $(b_n)_{n=0}^\infty$ is bounded.

Prove that whenever $n$ and $m$ are natural numbers such that $m > n$, then we have $a_{m} > a_{n}$

Suppose that $(a_{n})_{n=m}^{\infty}$ is a convergent sequence of real numbers. Then $(a_{n})_{n=m}^{\infty}$ is also a Cauchy sequence.

What is the number of all compositions of $n$ in which the first part is not $2$?

Derive Likelihood Ratio test for testing $H_0: \mu=\sigma^2$, $H_1: \mu \not= \sigma^2$.

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