When a limit exists, It is Unique - Proof

Jesus Christ is NOT white. Jesus Christ CANNOT be white, it is a matter of biblical evidence. Jesus said don't image worship. Beyond this, images of white Jesus are not just blasphemous and criminal, white Jesus is from Satan ( the imposter.) Why? Let's look at what Satan does:
1) He is incredibly narcissistic and promotes himself shamelessly.
2) He misleads and confuses.
3) He pushes people away from Jesus Christ God, the Holy Trinity, the one and only messiah. White Jesus does all three of the above and more -- matching the ways of Satan.

Statues of Christ are equally offensive to God the Christ. While money is the biggest idol, Jesus spoke sufficiently against carved images.
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You can also find me on Tik Tok @reuslovesmath and @polarpiny

In this video, I show you how to prove the uniqueness of a limit for functions.

[itstoogooditswaytoogood]

this video feels like you are teaching me the plan for a bank heist

[kiruvv]

can i solve it with giving two limits epsilon/2 ? and thank you this was helpful!!

[high_fly_bird]

Actually it is clearly explained though i can basically feel that you do not have enough air. Thank u very much, i'm in my first year of university in Saint-Petersburg and i really needed this.

[samuelgarcez]

This video is just perfect, thano you very much! You made me understand the proof in Spivak's Calculus ( I suppose you also saw it there ). Let me ask you, you is your face hidden? In one of your answers you indicated there is a video about it but I can't find it. God bless you!

[johanroypaul]

Dear Polar Pi,
How can we conclude that there is an epsilon which is greater than both f(x) -l as well as f(x)-m for different delta. δ1 and δ2. From the definition ?

[MarkFingerboard]

your suggested videos at the end completely cut off the end of the proof. You should post ads after you complete the proof...

[andreajose]

Why don't you have any subscribers ?

Edit : I subscribed. Also, your vids are great but the shadows are kinda annoying.

[rawdhatul_fawaid]

I can absolutely realte to this desmonstration tnx a looot maaan !!!

[sebahattinsaral]

video so good he had to do the intro twice

[ammarbamhdi]

Hi there, Thanks for your helpful video.


But I've got a small question,

Why don't we stress Epsilon to be Epsilon sub1 and Epsilon sub2 as we did in the delta part?

[SreeramPeela]

at 7.03 why |l-m| = |l-f+f-m| became |l-m| <= |l-f|+|f-m|?

[johanroypaul]

Dear Polar Pi,
1)How did you come to the idea of using law of contradiction to prove this?
2)Also why use the half of difference between l and m as your epsilon?

[nic_]

If Lt x-->a *f(x)* exists finitely, then prove that it is unique.
If possible, suppose
Lt x-->a *f(x)* = l & Lt x-->a *f(x)* =l' where l=l'
Plz tell what going on in this question...

[frankzhang]

what if approaches to infinite，how to prove

[alikasim]

awesome explantion u kind of lifted a burden from head

[thatdude_]

only in a topological hausdorff space though ;p

[gord]

thank you very much. Clear and clean. Like and suscribe; thank you ¡¡¡¡¡