Bijective Functions and the Continuum Hypothesis

This video is largely about bijective functions. Specifically why bijective functions have inverses, why bijective functions can be used to show two sets are the same size and how the continuum hypothesis can be written as a statement about bijections.

Chapters:
0:00 - Introduction
01:02 - Definitions
03:32 - Inverses
05:28 - Cardinality
08:29 - Continuum Hypothesis

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In-video references
1. An Introduction to Set Theory (William A. R. Weiss) - Available online for free.
2. Concepts of Modern Mathematics (Stewart) - https://amzn.to/3zIJyut
3. Basic Real Analysis (Anthony W. Knapp) - Available online for free
4. Foundations of Mathematics (Stewart and Tall) - https://amzn.to/3JVY0UJ
5. Cohen, P.J., 1964. The independence of the continuum hypothesis, II. Proceedings of the National Academy of Sciences of the United States of America, 51(1), p.105.

FAQ : How do you make these animations?
Animations are made in Apple Keynote which has lots of functionality for animating shapes, lines, curves and text (as well as really good LaTeX). Editing and voiceover work in DaVinci Resolve.

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Thank you so much, I hope you find the content useful.

• #education
• #functions
• #set_theory
• #set_cardinality
• #continuum_hypothesis
• #bijective_function