How Many Infinites Exist? ♾️ Cantor's Theorem

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Archimedes Tube

Published on Jan 28, 2021
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HOW MANY DIFFERENT INFINITE ARE THERE? WILL THERE BE AN INFINITE GREATER THAN ALL THE OTHERS? In this video we are going to study CANTOR'S THEOREM, which answers the previous questions. There are an infinite number of different infinities. What's more, we will also see CANTOR'S PARADOX that arises from considering the set of all sets. A real paradoxical monster. ⚠️ This video contains demonstrations. ---------------------------------------------------------------------------------------------------------- ????RECOMMENDED BIBLIOGRAPHY For readers approaching infinity for the first time, the best references can be found in Martin Gardner's books. MATHEMATICAL CARNIVAL. Martin Gardner. Alianza Editorial ➡️https://amzn.to/3qU7Zzs In chapter 3 "aleph 0 and aleph 1" we can see an approximation to these cardinals and the demonstration that they are different. M. Ram Murty and Brandon Fodden, ????Hilbert's Tenth Problem: An Introduction to Logic, Number Theory, and Computability (Student Mathematical Library) ➡️https://amzn.to/2XjwNnP A highly recommended book on the history of infinity is: Brian Clegg, ????A Brief History of Infinity: The Quest to Think the Unthinkable ➡️https://amzn.to/3pYjG7J The proof we give that for finite sets with cardinal n the cardinal of its power set is 2 raised to the power n I found in Arthur T. Benjamin, Jennifer J Quinn, ???? PROOFS THAT REALLY COUNT. THE ART OF COMBINATORIAL PROOF. English: https://amzn.to/2MfIVV1 ---------------------------------------------------------------------------------------------------------- ???? More Math books ➡️ https://www.amazon.es/shop/archimedes... Feel free to leave us comments with your questions. And if you liked the video, like and subscribe! :D http://bit.ly/ArchiSub ???? Follow us on Instagram! http://bit.ly/InstaSub ????Twitter: / archimedestub ???? Facebook: / archimedestub The links included in the bibliography are affiliate links. If you purchase any of the books through these links, we may receive a small commission from that sale. This WILL HELP ARCHIMEDES TUBE continue to move forward, but this will not have any effect on the price at which you buy it, which will be the same.

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