Absolute Value Definition of a Bounded Sequence | Real Analysis

The definition of a bounded sequence is a very important one, and it relies on a sequence having a lower an upper bound. However, we can also state the definition of a bounded sequence with only a single bound - namely an upper bound on the absolute value of the terms of the sequence. If there exists a real number that is greater than or equal to the absolute value of every term in a sequence, then the sequence is bounded, and the converse is true as well. As in: if a sequence is bounded then there exists a real number greater than or equal to the absolute value of every term in the sequence. We prove this equivalent definition of a bounded sequence in today's real analysis video lesson!

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THANK YOU SO MUCH FOR YOUR They are so helpful.

[krasimirronkov]

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

[ayatifouti]

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

[stachi-jb]

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