The definition of a Cauchy sequence (u_n) is:
(★) ∀ε>0. ∃n. ∀p,q≥n. |u_p − u_q| < ε
But it can also be given as the equivalent:
(☆) ∀ε>0. ∃n. ∀r≥n. |u_r − u_n| < ε
This seems a bit simpler, if less symmetric. Is there some reason nobody ever seems to write it that way?
(★) ∀ε>0. ∃n. ∀p,q≥n. |u_p − u_q| < ε
But it can also be given as the equivalent:
(☆) ∀ε>0. ∃n. ∀r≥n. |u_r − u_n| < ε
This seems a bit simpler, if less symmetric. Is there some reason nobody ever seems to write it that way?
October 17, 2025 at 8:34 AM
The definition of a Cauchy sequence (u_n) is:
(★) ∀ε>0. ∃n. ∀p,q≥n. |u_p − u_q| < ε
But it can also be given as the equivalent:
(☆) ∀ε>0. ∃n. ∀r≥n. |u_r − u_n| < ε
This seems a bit simpler, if less symmetric. Is there some reason nobody ever seems to write it that way?
(★) ∀ε>0. ∃n. ∀p,q≥n. |u_p − u_q| < ε
But it can also be given as the equivalent:
(☆) ∀ε>0. ∃n. ∀r≥n. |u_r − u_n| < ε
This seems a bit simpler, if less symmetric. Is there some reason nobody ever seems to write it that way?
June 14, 2024 at 1:41 AM
May 27, 2024 at 3:10 AM
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June 25, 2024 at 4:17 AM
June 18, 2024 at 12:37 AM
and Van der Poorten conjectured that for any $\epsilon >0$ there is a effectively computable constant $C(\epsilon),$ such that if $ \vert u_n \vert < (\max_i\{ \vert \alpha_i \vert \})^{n(1-\epsilon)}$, then $n< (\max_i\{ \vert \alpha_i \vert [2/3 of https://arxiv.org/abs/2504.09519v1]
April 15, 2025 at 6:05 AM
and Van der Poorten conjectured that for any $\epsilon >0$ there is a effectively computable constant $C(\epsilon),$ such that if $ \vert u_n \vert < (\max_i\{ \vert \alpha_i \vert \})^{n(1-\epsilon)}$, then $n< (\max_i\{ \vert \alpha_i \vert [2/3 of https://arxiv.org/abs/2504.09519v1]
May 11, 2024 at 4:17 AM
May 29, 2024 at 3:50 AM
May 28, 2024 at 12:44 AM
May 5, 2024 at 3:03 AM
April 25, 2024 at 3:22 AM
this paper, we solve a conjecture of Erd\H{o}s and Graham, which asks whether $$ \liminf_{n\to\infty} a_n^{\frac{1}{2^n}} < \lim_{n\to\infty} u_n^{\frac{1}{2^n}} = c_0 = 1.264085\ldots. $$ We prove this conjecture using two approaches. The first is [2/3 of https://arxiv.org/abs/2503.12277v1]
March 18, 2025 at 6:04 AM
this paper, we solve a conjecture of Erd\H{o}s and Graham, which asks whether $$ \liminf_{n\to\infty} a_n^{\frac{1}{2^n}} < \lim_{n\to\infty} u_n^{\frac{1}{2^n}} = c_0 = 1.264085\ldots. $$ We prove this conjecture using two approaches. The first is [2/3 of https://arxiv.org/abs/2503.12277v1]
May 26, 2024 at 4:08 AM
詳細はこちら：https://create.fortnite.com/news/how-we-improved-the-speedway-race-template-in-fortnite-with-verse-persistence-and-more
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June 25, 2024 at 2:22 PM
詳細はこちら：https://create.fortnite.com/news/how-we-improved-the-speedway-race-template-in-fortnite-with-verse-persistence-and-more
discord.com/channels/626...
#FORTNITE #フォートナイト #クリエイティブ #U_N
discord.com/channels/626...
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