Least upper bound proof
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.
Least Upper Bound Property: • Least Upper Bound Prop...
Dedekind Cuts: • Construction of the Re...
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Пікірлер: 19
I love how he approaches set theory! Very good!
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!! 🔥🔥🔥🔥
Please start lectures on discrete mathematics!
@drpeyam
4 жыл бұрын
Nooooo 😭😭😭😭😭
@johnclever8813
4 жыл бұрын
Dr Peyam Do Fourier Analysis!
Ok. Thank you very much.
Shocked
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.
@sebmata135
4 жыл бұрын
Cuts are actually defined the way you say. For simplicity, we just deal with the lower cut. You should read an analysis book for more details.
That's a very beautiful idea! Do you know who came up with it first?
@drpeyam
3 жыл бұрын
Dedekind maybe?
what field of math does this come under?
@drpeyam
4 жыл бұрын
Analysis and Set Theory
Can someone tell me what is a cut?
@drpeyam
4 жыл бұрын
Real Numbers Construction kzread.info/dash/bejne/jIuG0LyhidmWd5M.html
@lasithanirmitha321
4 жыл бұрын
Thank you Dr. Peyam
hi, I am also a math teacher
@162chetan
2 жыл бұрын
Than Wtf you are doing here... Just Go and teach the Maths
@162chetan
2 жыл бұрын
😝