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Hidden in this question is a lot of fascinating mathematics. Puzzle through and gain a greater appreciation for the simple act of counting. In this video, we will use our axioms to demonstrate how to construct functions and how we use them to robustly define counting. Last time, we defined the axioms of ZF and I highly recommend you watch that video first. Video making is something I’ve wanted to get into for a while.

Solution is what you seek? Will you succeed? Need to grow my channel. You can help by sharing my videos. To all those who watched and shared my last video, thank you! Write to me through the link in my website to get in touch. Special thanks to all those who supported me on Buy Me a Coffee! Comment below with any feedback you think will improve my content.

If you’d like to see more please consider supporting me on Patreon. Already, I’ve had lots of great feedback and really appreciate all the nice words. Solved — that’s how I’d like to feel about the video-making process but I’m not there yet. Try as I might, these videos take a really long time for me to make. Reverse engineering the mathematics to make it accessible to a wide audience is a slow process. Slug pace, some might say.

00:00 - Intro
01:28 - Motivation
05:30 - Ordered Pairs
17:51 - Functions
20:56 - Thank You! And Patreon!
21:36 - Function Types
26:05 - Counting
27:48 - Counting is Well-Defined
36:45 - Closing Remarks

*Correction: As stated, I show the 1-set, {{}}, where in fact I should show the 2-set {{},{{}}}.

**I have no idea why my footage is so blurry from around the 26-minute mark. Apologies!

All music by Danijel Zambo.

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