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Cantor's Theorem on the cardinality of a set and of its powerset (countable and uncountable sets)
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I am a professor in the Computer Science department at the University of Cambridge and I teach the last part of the Discrete Mathematics course (see playlist and syllabus below).
This video is a footnote to one of those Discrete Maths lectures in which I hinted at Cantor's Theorem, assuming you had already seen it, and I used its result without proving it. Today we prove it.
This theorem is a rather deep result about the foundations of set theory and the cardinalities of sets (by one of the founders of the discipline) and it took a genius to get to it; but it's one of these intellectual things of beauty that, once you have the right tour guide, can be grasped even by a smart ten-year-old. I am hoping to be that guide for you, and if you are actually ten years old then please be sure to let me know in the comments and you'll make my day ;-)
My Discrete Maths course at Cambridge (Regular Languages and Finite Automata):
This video is a footnote to one of those Discrete Maths lectures in which I hinted at Cantor's Theorem, assuming you had already seen it, and I used its result without proving it. Today we prove it.
This theorem is a rather deep result about the foundations of set theory and the cardinalities of sets (by one of the founders of the discipline) and it took a genius to get to it; but it's one of these intellectual things of beauty that, once you have the right tour guide, can be grasped even by a smart ten-year-old. I am hoping to be that guide for you, and if you are actually ten years old then please be sure to let me know in the comments and you'll make my day ;-)
My Discrete Maths course at Cambridge (Regular Languages and Finite Automata):
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