Least upper bound proof
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4 жыл бұрынProof 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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@NotoriousSRG 4 жыл бұрын
I love how he approaches set theory! Very good!
@ReCaptchaHeinz 4 жыл бұрын
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!! 🔥🔥🔥🔥
@azhakabad4229 4 жыл бұрын
Please start lectures on discrete mathematics!
@drpeyam 4 жыл бұрын
Nooooo 😭😭😭😭😭
@johnclever8813 4 жыл бұрын
Dr Peyam Do Fourier Analysis!
@dgrandlapinblanc 2 жыл бұрын
Ok. Thank you very much.
@thedoublehelix5661 4 жыл бұрын
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.
@jonasdaverio9369 3 жыл бұрын
That's a very beautiful idea! Do you know who came up with it first?
@drpeyam 3 жыл бұрын
Dedekind maybe?
@u.s.r.00 Жыл бұрын
Shocked
@alwysrite 4 жыл бұрын
what field of math does this come under?
@drpeyam 4 жыл бұрын
Analysis and Set Theory
@lasithanirmitha321 4 жыл бұрын
Can someone tell me what is a cut?
@drpeyam 4 жыл бұрын
Real Numbers Construction kzfaq.info/get/bejne/kL2Cob2ZvtyUd2Q.html
@lasithanirmitha321 4 жыл бұрын
Thank you Dr. Peyam
@MathswithMuneer 4 жыл бұрын
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
😝
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