A Bounded Monotonic Sequence is Convergent Proof (Real Analysis Course #20)

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Here we will prove that a bounded monotonic sequence is convergent. This is a great proof taking advantage of the supremum and giving us a quite a famous result! Enjoy.

#realanalysis #brithemathguy #math

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Disclaimer: This video is for entertainment purposes only and should not be considered academic. Though all information is provided in good faith, no warranty of any kind, expressed or implied, is made with regards to the accuracy, validity, reliability, consistency, adequacy, or completeness of this information.

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BriTheMathGuy

I'm really impressed with the speed he writes a reflected version of those sentences

ismailsheik

It's been a while, I'm glad you're back.

usernamehere

We need you to continue Real analysis tutorial. Thank you

asmrEveryday

It is awesome to see you back as well. I'm actually in my first year as a mathematics student and your vids have been an awesome source of learning for me. thanks!

canadianmaple

This playlist is a gem, please make more videos! Thank you

hannananan

please continue this real analysis series!

axog

Can you please make videos on the "tests" and their proofs in real analysis? Like the limit test, root test, comparison test, etc...

mathgeek

Sorry, isn't there a small typo in the proof? It does not change the result but still: last line, second to last inequality should not be strict as you imposed that the sequence is not strictly monotonic (in the line above the inequality is not strict).

danilolewanski

I have had the idea to do this kind of series for analysis. Short videos of the most important proofs. Thanks man.

Mr_mechEngineer

Nice video! I think by bounded, you need |a_n| \leq B because the secquence a_n = - n is not bounded but has the property a_n \leq B for some B.

Also, I dont understand why there is an if and only if. You only proved the if part, but the only if is not true I guess. Not every convergent sequence is monotonic and bounded. Take for example a_n = (-1)^n /n. It is a convergent sequence to 0, bounded, but not monotonic.

Keep up the good work, love your vids! 😊

bramlentjes

You said Am is less than a - epsilon but wrote Am > a - epsilon.

kaisiasima

your face is kinda distracting i was watching you the whole time

meenugoyal-csjr

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