Proof that every convergent sequence is bounded

A proof that every convergent sequence is bounded.

[bbsilva]

6 years later and still helping people! Thanks.

[danieltrigo]

Dude, I really appreciate your videos, they are a great contribution to my education. Thank you very much, and please keep going, your work is excellent!!!

[kiruvv]

thank you so much that was so helpful, i was strugeling with this!! thanks from algeria <3

[dakshanakanapathy]

Thank you sir it is very helpful to me

[snowyelsa]

Thank you very much! Got exam tomorrow, your video really helped! :)

[thedounut]

I was doing this and literally wrote down that maximum arguement for n<N but was having trouble realizing whether or not I was allowed to do that. So close, so very very close. Glad my ideas are validated. Thank you very much!

[ananyasharma]

Is Converse valid ??? Every bounded sequence is convergent ??? Here it is not monotonic

[Pandafist]

Thanks for a clear and correct proof! Sequence proofs using the technique of max{} can be a little tricky and I've seen at least two professor incorrect solutions to this problem.

[cloudhuang]

Excuse me sir, isn't there any possibility that a convergent sequence "blows up" divergently in some of the first "N" terms so that makes the sequence unbounded?

[gabrielmccartney]

why is it still enough to consider only epsilon = 1?

[iOSGamingDynasties]

Why |a_n| <= max{|a_1, ..., a_N} for n<= N? Is there a specific reason that you chose n<= N? I know that it might be related to the definition of limit of a sequence but I don't understand how to picture it...

[EmapMe]

Intuitively, why couldn't the terms of the sequence be infinity for some terms, then still approach some value when n approaches infinity?

[monishadamodaran]

why do we choose epsilon as 1? Can we choose any other number greater than 0?

[konohaninja]

How can |an| <= |aN| for all n<=N? E.g. an=1/n, for n<=N it follows that an > aN. What am I missing?

[ShahidHussain-wjvx]

ur video is helpful but....it is not so clear to see...plz don't use black backgrounds

[guydude]

Does this also apply for complex numbers? If not, how would the proof differ for them?

[muhammedqadr]

The conversly is true ?
we have a theorm say ( every bounded monotone sequence is convergant )

[bilalwajid]

Every convergent sequence is bounded what about is converse? Prove both statements with examples

[popsicle]

How do we know |an|<=max{|a1|, ..., |aN|}... when I visualize it's obvious but I can't really prove it. Is this something from the definition of a convergent sequence or...?

[noddyd]

How do we know that an is less than or equal to max of a1....aN for n less than equal to N