Artificial Intelligence, Robotics, Chat bots - ChatGPT Message Board

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Technology Stocks : Artificial Intelligence, Robotics, Chat bots - ChatGPT

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From: Frank Sully	5/2/2025 4:17:03 PM
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Off Topic Discussion: Mathematics Of Infinity In a discussion I'm having with one of the boards posters, we touched upon infinity and the existence of irrational numbers such as the square root of two. In a debate between Cantor and Kronecker circa 1850 the modern theory of infinity was developed by Cantor, an unknown, and denied by the well-established Kronecker. Cantor constructed the real numbers, including irrational numbers such as square root of two, as the limit of rational numbers (fractions) getting closer and closer (technically, equivalence classes of convergent Cauchy sequences). He was then able to prove that the set of real numbers is uncountable, unlike the rationals. A set is "countable" if it can be put into a one-to-one correspondence with the set of counting numbers 1, 2, 3, 4, ... Thus the Reals have a higher degree of infinity than the rationals. His proof of uncountability uses a famous "Diagonalization Argument" I learned in college. See six minute video below. youtu.be

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