Can Mathematicians Code? The Intermediate Value Theorem
Автор: Sheafification of G
Загружено: 2024-05-01
Просмотров: 31594
Описание:
The IVT is introduced in every first-year differential calculus course, and gives a way of proving the existence of solutions to various equations... but does it say anything about how we can algorithmically find such a solution?
Mathematicians don't program, they prove... but can we extract algorithms from proofs?
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Timestamps:
00:00 - I want to apologise
00:43 - What is the IVT?
01:52 - Elementary proof
04:19 - Algorithm I
04:45 - Objections to the proof
05:03 - Abstract proof
05:20 - Step 0: Continuity (in detail)
06:28 - Step 1: Connectivity
07:42 - Step 2: The abstract IVT
08:18 - Step 3: Intervals are connected
09:18 - Algorithm II
09:51 - The truth about proof II
10:50 - Conclusion
11:00 - Thx 4 watching
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