Proof: Limit of a Function is Unique | Real Analysis

[@WrathofMath]

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[@Podzhagitel]

The false start at the beginning made me feel like I was having a stroke

[@WrathofMath]

I edit my videos so meticulously, can't believe I missed that!

[@CamQuilici]

Please never stop making these videos. Currently in Real Analysis and these videos are so helfpul!

[@WrathofMath]

Thank you! Good luck in class!

[@danielobanla5466]

We previously introduced the defin... We previously introduced the formal definition 😅

[@punditgi]

A nifty little proof! Nicely done. 😊🎉

[@WrathofMath]

Thanks muchly!

[@officersmiles9114]

Thanks, great video. Super clear and concise.

[@dipmondal6416]

Sir your videos are so helpful & very conceptual as well. Please never stop making this kind of videos

[@WrathofMath]

Thank you, I will continue the grind!

[@michaelklein6098]

Really nice explanition. However in this general form the statement is not correct. If we consider A = {0}, c = 0 and f : A -> R with f(0) = 0, we have that the limit of f(x) as x approaches zero is ANY value. Proof: Let Epsilon > 0 and chosse delta = 1. Now there is no x in A such that 0 < |x-0| = |x| < 1 = delta, because 0 is the only value in A. Therefore the implication of the epsilon-delta defintion is true for any value of L. (A -> B is true if A is false). You can fix this problem by assuming that c is in the interior of A.

[@darasimidada2194]

Thank youu very much man

[@WrathofMath]

You're welcome!

[@Jdhh829]

I still dont understand why we take the delta to be the minimum ?

[@shifanafathima7364]

Because if you take delta to be max that is suppose if delta1 is max then delta will be equal to delta1 also delta2

[@divyadharshinid7921]

Such a subtle one🩷

[@WrathofMath]

Thanks for watching!