Ben Shapiro Just EXPOSED Tucker Carlson's Dirty Secret & Now It's Going Viral!
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www.youtube.com/watch?v=u_n-...
Ben Shapiro Just EXPOSED Tucker Carlson's Dirty Secret & Now It's Going Viral!
YouTube video by SaharTV
www.youtube.com
November 25, 2025 at 1:08 AM
Ben Shapiro Just EXPOSED Tucker Carlson's Dirty Secret & Now It's Going Viral!
www.youtube.com/watch?v=u_n-...
www.youtube.com/watch?v=u_n-...
今週の星座タロット ２０２５/１１ 第２週【タロットリーディング 四国めたん読み上げ】
YouTube video by ドクまんじゅうの姿ch iinosan-k
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November 10, 2025 at 5:43 PM
Proof of equivalence: (★) ⇒ (☆) is trivial. For (☆) ⇒ (★), given ε, apply (☆) to ε/2, giving n such that if r≥n then |u_r − u_n| < ε/2; now if p,q≥n, then |u_p − u_q| ≤ |u_p − u_n| + |u_n − u_q| < ε/2 + ε/2 = ε. ∎
(This proof is valid constructively and doesn't use Choice.)
(This proof is valid constructively and doesn't use Choice.)
October 17, 2025 at 8:34 AM
Proof of equivalence: (★) ⇒ (☆) is trivial. For (☆) ⇒ (★), given ε, apply (☆) to ε/2, giving n such that if r≥n then |u_r − u_n| < ε/2; now if p,q≥n, then |u_p − u_q| ≤ |u_p − u_n| + |u_n − u_q| < ε/2 + ε/2 = ε. ∎
(This proof is valid constructively and doesn't use Choice.)
(This proof is valid constructively and doesn't use Choice.)
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?
#クリエイターサポートコード を変更したので新しい #フォートナイト の #プロフィール を共有します。
fortnite.com/@ugitonjp
#FORTNITE #FN #フォトナ #クリエイターサポート #クリサポ #クリサポコード #U_N
fortnite.com/@ugitonjp
#FORTNITE #FN #フォトナ #クリエイターサポート #クリサポ #クリサポコード #U_N
October 17, 2025 at 6:07 AM
#クリエイターサポートコード を変更したので新しい #フォートナイト の #プロフィール を共有します。
fortnite.com/@ugitonjp
#FORTNITE #FN #フォトナ #クリエイターサポート #クリサポ #クリサポコード #U_N
fortnite.com/@ugitonjp
#FORTNITE #FN #フォトナ #クリエイターサポート #クリサポ #クリサポコード #U_N
I think the better approach is via Weyl sequences: These are sequences of normalized u_n in your HS, that converge weakly to 0, but for your operator A, the sequence A u_n converges in norm to lambda u_n. If that exists, lambda is in the (essential) spectrum of A. This is math for "wave packet".
October 15, 2025 at 4:38 PM
I think the better approach is via Weyl sequences: These are sequences of normalized u_n in your HS, that converge weakly to 0, but for your operator A, the sequence A u_n converges in norm to lambda u_n. If that exists, lambda is in the (essential) spectrum of A. This is math for "wave packet".
‘Your Countries Are Going to Hell’: Trump Airs His Grievances at the U.N. In a meandering address, President Trump rebuked global institutions and complained about immigration, environmentalists, windmills and more.. @cosmicmeta.ai #U_N
https://u2m.io/YgYNf6Uj
https://u2m.io/YgYNf6Uj
September 23, 2025 at 6:17 PM
‘Your Countries Are Going to Hell’: Trump Airs His Grievances at the U.N. In a meandering address, President Trump rebuked global institutions and complained about immigration, environmentalists, windmills and more.. @cosmicmeta.ai #U_N
https://u2m.io/YgYNf6Uj
https://u2m.io/YgYNf6Uj
(๑•̀ㅂ•́)و✧ ﾖｼｯ!
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August 15, 2025 at 6:46 AM
(๑•̀ㅂ•́)و✧ ﾖｼｯ!
#FORTNITE #FN #フォートナイト #フォトナ #PlayStation5 #PS5 #クリエイティブ #クリエ #キャプチャー #Shorts #ショート #クロスプレイ #ゲーム #テレビゲーム #ビデオゲーム #YouTube #配信切り抜き #切り抜き #U_N
#FORTNITE #FN #フォートナイト #フォトナ #PlayStation5 #PS5 #クリエイティブ #クリエ #キャプチャー #Shorts #ショート #クロスプレイ #ゲーム #テレビゲーム #ビデオゲーム #YouTube #配信切り抜き #切り抜き #U_N
August 5, 2025 at 7:42 AM