Proof: Supremum of {1/n} = 1 | Real Analysis

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The supremum of the set containing all reciprocals of natural numbers is 1. That is, 1 is the least upper bound of {1/n | n is natural}. We prove this supremum in today's real analysis lesson using the epsilon definition of supremum!

Thanks to Nasser Alhouti, Robert Rennie, Barbara Sharrock, and Lyndon for their generous support on Patreon!

I hope you find this video helpful, and be sure to ask any questions down in the comments!

+WRATH OF MATH+

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Son geniales tus videos, saludos desde México.

davelop
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Thanks for the helped, it helped me clarify some stuff before the exam ☠

larubiano
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Sir, at 3:01 where you wrote 1- E > 1 what if we write 1 - E > m for any m € N .
If yes, then can you please tell how will we explain it further !!

vaishnaviatreya
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Somebody please ans me - glb and lub of mn/m^2 + n^2, m belongs to reals and n belongs to natural number.

tania
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Could you please explain petersen graph in detail

simasalari
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if upperbound is inside set then its neccesary that it is supremum? i think yes . as a-epsilon will be alwys less yhan a

Aman_iitbh
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Is it necessary that sup A and inf A to be natural numbers

sarala.d