Proof: Limit Law for Quotient of Convergent Sequences | Real Analysis

We prove the limit law for the quotient of convergent sequences. If a_n converges to a and b_n converges to b, then the sequence a_n/b_n converges to a/b, provided that b isn't 0, and each b_n is not 0. Put simply, the quotient of convergent sequences converges to the quotient of their limits. This is a slightly tricky proof using the epsilon definition of a convergent sequence, and some fun absolute value inequality manipulations!

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[christianpotts]

Thanks! The limit law videos are great.

[seven.]

fantastic video! I'm finding that in reading proofs online or trying to prove them myself i'm left feeling hopeless in where the aspects of the proof come from like why use this law and not another - why create this inequality and not another - etc. This was a great explanation of both the proof and motivations of the proof so it solved this issue for me - thank you!

[spiderjerusalem]

this is more satisfactory than that of abbott's approach. Thanks in advance!

[loo]

5:26 Can't you make |bn - b| smaller than ε*|b|*|k| where k is the upper bound of bn and you know |bn| < |k|?

[geno]

Great Video! Well explained and really well made!
Also a quick question, wouldn't this method of proof require that we also proof the Limit Product Laws for convergent sequences? I've seen other proofs without that, but this seems like a lot more cleaner and simple proof.
As always, thanks for the great video!

[rivaschristian]

How did you find the epsilon absolute of b squared over w

[akavyascv]

If b is zero then sequence an/ bn diverge?

[joshmckinney]

Where were you when I was taking undergrad analysis??

[abdulazeezbamidele]

There are some ambiguous fact which I'm yet to comprehend

[parasmittal]

keep doing what you are doing, really good work

[malawigw]

I understand algebraically why |b_n| > |b| / 2 but not conceptually