A Stroll Through Cecily's Sets: A Children's Book About Set Theory

This is a children's book designed to introduce students to set theory, with an emphasis on strange concepts like empty sets, infinite sets, uncountable infinite sets, and more. This book is designed to make kids ask questions about math and set theory, not answer them. So if you don't want more questions, don't buy this. This book does explain what it easily can about set theory, it just introduces more things than it has time to explain!

This book introduces abstract mathematics. Not counting, arithmetic, shapes, geometry, or even statistics. This isn't a book about science, physics, technology, or biology. It is a math book. It introduces fundamental math concepts in a visually appealing and gentle way without getting too hung up on the details.

Normally set theory at this level is reserved for college, or a few lucky high school classes. This is not without reason: set theory is mostly used in proofs which are not often given to students until college. But proofs are just formal explanations for why things are true. Many US students only see proofs in geometry where set theory is not needed and the proofs are unlikely to be useful in the future: even if they pursue a stem degree. This may be sufficient for high school algebra, but leaves students unprepared and ignorant of what college level math is really like.

Teaching students proper set theory is difficult, especially children, but just the basics can be the difference between being able to formally explain a proof or not. This book gives a resource to help introduce these concepts to children, even if it is not a complete resource.

QUOTES

Scott Aaronson: "It's extremely cute. It strikes me as a much better version of "New Math," which was an effort in the 1960s to start elementary school kids off on the right foot by teaching them about subsets, super sets, power sets, etc."

FAQ

Who should buy this book?

• Parents who want to encourage their children to learn more about math.
• Parents who are willing to learn with their children when they ask questions (unless you are a mathematician, this likely touches on some concepts you don't know or haven't thought about in a while).
• Teachers brave enough to introduce set theory or more esoteric concepts to their students.
• Children who want a pretty looking picture book that insists on some strange and peculiar things.

Who should not buy this book?

• People who don't want to answer hard questions.
• People who don't want to help children with new vocabulary (it does its best to avoid technical terms, but some still made it in).
• People who have don't like their intuitions questioned.

How much does this cover?

It has 25 illustrated pages covering about one concept per page. It has a few extra non picture pages of context as well. It covers basic set operations, goes up to infinity even discussing some of the weird quirks of infinity, discusses how to build pairs out of sets, and more. It does not define functions, set builder notation, or logic in general.

Can I use this as a textbook to teach set theory?

NO! This is a brief gentle introduction to set theory. Someone should make a much longer set theory book if we want to actually teach this to elementary grade children. This would be doable, but would require a very different style than this book.

Will this help my kid learn algebra (arithmetic, etc)?

Probably not, unless someone is trying to prove why algebra and arithmetic work to them!

What is set theory useful for?

Simply put: math. But this also includes Computer Science (like data structures and algorithms), statistics, chemistry, physics, philosophy, and most kinds of engineering. If you want to prove something mathematically, you need set theory.