Absolute Value Definition of a Bounded Sequence | Real Analysis

[@red3987]

THANK YOU SO MUCH FOR YOUR VIDEOS!!!!!!!! They are so helpful.

[@WrathofMath]

My pleasure! Glad you've found them useful, let me know if you ever have any questions! Lots more analysis videos will come this summer most likely!

[@yousufalsalmi1241]

That was helpful. thanks

[@mahmoudalbahar1641]

Many thanks for this good video.

[@WrathofMath]

My pleasure, thanks a lot for watching!

[@ayatifouti3103]

How can we prove that every finite sequence has a partial sequence?

[@krasimirronkov17]

The video was awesome. My question is can you make a proof on why a sequence that is both bounded and monotonic is convergent?

[@WrathofMath]

Thank you! And you're in luck. I just made a lesson on the squeeze theorem, and the monotone convergence theorem is up next! In the meantime, be sure to give it a swing yourself! If a sequence is bounded, we can consider the bounded set of values the sequence takes on, which must have a supremum. Then consider using the epsilon definition of supremum. kzbin.info/www/bejne/onTToHiNf7eMhM0 These tools can take care of the increasing sequence case.

[@WrathofMath]

It will release publicly later this week, but here is a link to view the lesson now: kzbin.info/www/bejne/an-4g3ejepxsjLc If you find it and the other real analysis lessons helpful, I'd tremendously appreciate you sharing the real analysis playlist [ kzbin.info/aero/PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli ] with anyone you know who may find it useful! I am focusing on real analysis lessons specifically this year, so I hope it will be a valuable playlist for many people!

[@stachi-j7b]

the more videos I watch of him the more he looks like Timothee Chalamet