I'm getting flashbacks of Baby Rudin's first chapter from this comment :) For anyone who wants to learn more about this: what the parent comment is describing

I'm getting flashbacks of Baby Rudin's first chapter from this comment :) For anyone who wants to learn more about this: what the parent comment is describing is the construction of natural numbers as cardinalities of sets. This is the (modified) Frege definition which avoids Russell's paradox - you can use that as a jumping off point for further dives into set theory and number systems. To define Peano arithmetic you start with a successor function, then an addition function, then multiplication, etc.