Proof and Problem Solving - Family of Sets and Indexed Family of Sets

adampanagos.org
A simple example that works with an indexed family of sets and associated notation.
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[@valeriereid2337]

Thanks very much for this excellent example. It certainly helps.

[@AdamPanagos]

Thanks for the kind words, I’m glad you enjoyed the video! Make sure to check out my website adampanagos.org for additional content (600+ videos) you might find helpful. Thanks much, Adam

[@yoshihirogyagi2121]

Thank you, Adam. Really good stuff.

[@AdamPanagos]

Glad you enjoyed, thanks for watching!

[@Bible7-7]

What is the results will be if index set is an empty set?

[@MariannaLeros]

Thanks for taking the time to make these videos! They are very informative and beneficial.

[@AdamPanagos]

Great, glad you found them useful. Thanks.

[@user-cc6wv2uc4l]

Thank you so much - nobody explains these...

[@hajerjm]

Can you please tell what's the Textbook used for this course? Thank you very much for these videos!

[@AdamPanagos]

The textbook used for the course is, "How To Prove It: A Structured Approach", 2nd edition by Daniel J. Velleman.
Another excellent resource for this type of material is, "The Book of Proof" by Richard Hammack. The later can be downloaded for free from the author:
www.people.vcu.edu/~rhammack/BookOfProof/Main.pdf
Thanks for watching,
Adam

[@miriamsantaniellp6177]

Crystal clear explanations!

[@AdamPanagos]

Thanks for the kind words, I’m glad you enjoyed the video! Make sure to check out my website adampanagos.org for additional content (600+ videos) you might find helpful. Thanks much, Adam

[@satyendrayaduwanshi1252]

Amazing explanation.. Thanks for this video..

[@AdamPanagos]

Glad you found the video useful, thanks for watching.
Adam

[@tomastomas4739]

Thanks the only video on CZcams that explains how to work with sets 👍

[@AdamPanagos]

Glad I could help, thanks for watching.

[@dilara2864]

Thanks 🙏🏽

[@AdamPanagos]

Thanks for the kind words, I’m glad you enjoyed the video! Make sure to check out my website adampanagos.org for additional content (600+ videos) you might find helpful. Thanks much, Adam

[@chemdah]

What is an indexed family of sets used for?

[@csmathster]

Every math class after calculus.

[@chandrapandey822]

Robert Nooney
It is extremely important in Topology and in complex analysis

[@cavelinguam6444]

Awesome

[@eufrosynie]

Thanks 💝

[@AdamPanagos]

You're very welcome, thanks for watching. Make sure to check out my website adampanagos.org for additional content (600+ videos) you might find helpful. Thanks, Adam.

[@jokerhhhify]

GREAT THANKS

[@AdamPanagos]

You're welcome, glad you like it.

[@limitsatinfinity4393]

But What are A_i , themselves?

[@AdamPanagos]

Each A_i is a set. As i changes, the set changes. Just an indexed collection of sets.