Least upper bound proof

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Proof of the Least Upper Bound Property

In this video, I present a very elegant proof of the least upper bound property. This proof really illustrates why Dedekind cuts are so nice.

  1. Dr Peyam
  2. peyam
  3. dr peyam
  4. blackpenredpen
  5. ross
  6. analysis
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Комментарии
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I love how he approaches set theory! Very good!

NotoriousSRG
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Maaaan I was meant to study this year's before, but it's now that you make me feel amazed by how cool is stuff. I always heard of "cuts to define R" but I never actually saw it from the beginning. Thank you! Keep on!! 🔥🔥🔥🔥

ReCaptchaHeinz
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Please start lectures on discrete mathematics!

azhakabad
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That's a very beautiful idea! Do you know who came up with it first?

jonasdaverio
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Quick nitpick: This doesn't matter at all but it really annoys me how we arbitrarily chose the cut to be infinite from below. We could've constructed the cuts so that they're infinite above and it would be the exact same so I think maybe we should have the real numbers be equivalence classes on upper and lower cuts. (I'm p sure each upper cut has a corresponding lower cut.

thedoublehelix
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what field of math does this come under?

alwysrite