Real Analysis #3 - The Completeness Property

The topic of this real analysis video is the Completeness Property (also know as the least upper bound property). We will need this for our discussion of the Real Numbers so I hope you enjoy the video!

#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.

[BriTheMathGuy]

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[hazelndlovu]

Finally useful Real analysis videos. Suggestion -Do more examples at the end.

[LukeSequ]

These are the best real analysis videos I can find!

[sinjini]

I was confused about why Q does not have the completeness property. And this video cleared my confusion. Thank you so much!

[izzywhippet]

You said that root 2 is an upper bound of the set defined on Q, but your earlier definition of bounds said that an upper bound on Set S has to be an element of S. But as you go on to say, root 2 is not in Q, so it is not in the set you defined either.

Have I misunderstood the definiton of bounds?

[cgfam]

Thank you so much. your 4 min video is way better than +30 min of others!!!

[AnhNguyen-zdbd]

So it means the set { x^2<2 | for all x belongs to Q} does not have the completeness property?
I don't get it, the supA is not necessarily contained in A, since if supA is contained in A we have MaxA=sup A. May you please explain more?
Thanks in advance.

[sibusisopgambu]

Thanks. Please keep making more videos ...

[supernova]

Does the supremum have to be in the set we're working with? Do the bounds have to be in the sets we're working with?

[jaygourley]

Is the word "has" equivocal in this lecture? It could also mean "is contained in."

[mariamary]

What's the completeness property of set IR?