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Section 1.1 What is this?

I’ve been trying to work my way though "Conceptual Mathematics" by Lawvere and Schanuel (herein "L&S") on my own and it’s been kind of difficult. Part of the problem is that I don’t have any feedback about whether my solutions to exercises are correct or not. In an effort to resolve this, I’ve decided to publish my solutions as I go through it so I can discuss them on social media.
With that in mind, it seemed like this would be a good opportunity for me to simulaneously learn how to work with PreTeXt. I’ve done a lot of work using for equations before but I’m expecting this content gives me some much needed practice rendering diagrams with the TiKz package.
To start, I went through my old notes on L&S from my first attempted reading. It looks like I made to to around session 11 before I started really getting lost. Furthermore, the erasable ink I had used to solve the exercises originally had faded significantly since I originally worked on this. Since I’m expecting one of my major difficulties with this to be recreating the diagrams, I figured restarting from the very beginning would be the best way forward.
I know myself better than to make promises about the rate I get through this, but part of me thinks it would be fun to do "cat theory on caturday". Giving myself a day of the week to finish by might give me the push I need to get it done. Besides, everything is better with cats.