Refactor SqueezeThm statement to include N parameter #18
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Hi Roger, sure, we can make an "eventually" version of the Squeeze Theorem. You've changed the definition, so now the proof breaks; can you fix it, and resubmit the PR? Best, AK |
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Hi Professor Kontorovich,
I'm so sorry I messed it up. I'm fixing it right now.
Best,
Roger
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Subject: Re: [AlexKontorovich/RealAnalysisGame] Refactor SqueezeThm statement to include N parameter (PR #18)
[https://avatars.githubusercontent.com/u/58564076?s=20&v=4]AlexKontorovich left a comment (AlexKontorovich/RealAnalysisGame#18)<#18 (comment)>
Hi Roger, sure, we can make an "eventually" version of the Squeeze Theorem. You've changed the definition, so now the proof breaks; can you fix it, and resubmit the PR? Best, AK
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Hello Professor Kontorovich, I believe Squeeze Theorem should be slightly altered. I believe it should be:
Let (an), (cn) be two sequences converging to ℓ, and (bn) a sequence. If ∀ n ≥ N, N ∈ N we have an ≤ bn ≤ cn, then (bn) also converges to ℓ.
Currently we don't have the constraint N, and it's just an ≤ bn ≤ cn for all n, which isn't what Squeeze Theorem is.
I actually had issue with this in latest homework, because I cannot use the sequence 1/n as part of my squeeze theorem, as when n= 0 it's invalid and the an ≤ bn ≤ cn doesn't work. Fixing the definition would allow it to work that way.
Thank you for considering this suggestion!