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Learning the foundations of math

Principles of Arithmetic and Geometry by Carl Allendoerfer

If you are looking for a book that begins before even numbers begin, then this is it.

The book starts with basic logic, then moves to define basic set theory very clearly, then proceeds to explain how set theory is the foundation of our whole number system, and finally moves to defining all elementary operations using what you've learned. He goes into great depth of defining all the various kinds of correspondences, cardinality, and other crucial ideas that usually get ignored early on.

Allendoerfer s... (read more)