Prove that for any positive integer $n$, there exist $n$ consecutive positive integers $a_1, a_2,...,a_n$ such that $p_i$ divides $a_i$ for each $i$,…

score 210 · Answer 8 · 2026-03-25 15:39:23

210

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Minimum Spanning Tree - How to Prove this Inequality?

Published on 25 Mar 2026 - 15:39

score 15k · Answer 9 · 2026-04-09 07:56:44

15k

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Proof of product rule for limits

Published on 09 Apr 2026 - 7:56

score 1.4k · Answer 10 · 2026-03-25 15:17:52

1.4k

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Proving the boundary of a disc is a circle

Published on 25 Mar 2026 - 15:17

score 158 · Answer 11 · 2026-03-28 04:35:41

158

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Let $a_n \rightarrow A$ and $b_n \rightarrow B$ as $n \rightarrow \infty$, with $a_n \leq b_n$ for all $n$. Show $A \leq B$.

Published on 28 Mar 2026 - 4:35

score 353 · Answer 12 · 2026-03-25 04:41:43

353

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Gradient descent proof: show that $f(x^k) - f(x^) \leq \|x^0 - x^\|_2^2/2\alpha k$

Published on 25 Mar 2026 - 4:41

score 146 · Answer 13 · 2026-04-11 08:09:47

146

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Personal experience in finding and writing proofs in general

Published on 11 Apr 2026 - 8:09

score 59 · Answer 14 · 2026-03-28 04:36:16

59

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Is this proof of the Sup and Inf of $S = \lbrace\frac{2}{n}\mid n \in\lbrace {1, 2, 3, 4,...}\rbrace\rbrace$ correct?

Published on 28 Mar 2026 - 4:36

score 733 · Answer 15 · 2026-04-01 00:26:38

733

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Finding and Proving the Supremum and Infimum of $X = \bigcup\limits_{n=1}^{\infty} [2n, 2n + 1]$

Published on 01 Apr 2026 - 0:26

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Suppose S1 and S2 are self-adjoint operators in L(V ) such that: T = S1 + iS2. Show that S1 = T1 and S2 = T2 where T1 and T2

Showing that a limit is false, did I prove it?

Proof confusion: Let $G$ be a group of order $2p$ , where $p$ is a prime greater than $2$. Then, G is isomorphic to $\mathbb{Z}_{2p}$ or $D_p$

Is it valid to reference the limit product proof when proving the quotient proof?

How can I show $q^k$ does not divide ${{n}\choose{q}}$ when $q$ is a prime factor of $n$ and $k$ is the largest integer such that $q^k$ divides $n$?

Stuck on trying to prove product rule for limits

Prove that for any positive integer $n$, there exist $n$ consecutive positive integers $a_1, a_2,...,a_n$ such that $p_i$ divides $a_i$ for each $i$,…

Minimum Spanning Tree - How to Prove this Inequality?

Proof of product rule for limits

Proving the boundary of a disc is a circle

Let $a_n \rightarrow A$ and $b_n \rightarrow B$ as $n \rightarrow \infty$, with $a_n \leq b_n$ for all $n$. Show $A \leq B$.

Gradient descent proof: show that $f(x^k) - f(x^) \leq \|x^0 - x^\|_2^2/2\alpha k$

Personal experience in finding and writing proofs in general

Is this proof of the Sup and Inf of $S = \lbrace\frac{2}{n}\mid n \in\lbrace {1, 2, 3, 4,...}\rbrace\rbrace$ correct?

Finding and Proving the Supremum and Infimum of $X = \bigcup\limits_{n=1}^{\infty} [2n, 2n + 1]$

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