How and where to learn the properties of numbers and really understand them? I am a university student and was reading through the first chapter of Rudin's Principles of Mathematical Analysis to improve my mathematical skills, but I was immediately stumped when the author started talking about rational numbers and the proof that `p^2 = 2` is not satisfied by any rational number `p`, and then he goes on about why it is so using an argument about odd and even numbers. This sort of made me realise how poor my understanding is of numbers, as well as many other basic fundamental axioms in math, when I could not even get past the first paragraph without getting confused... XDDD I want to relearn the numbers and other basic math properties from scrath -- what book would be best to do that? I want a rigorous book like rudin which will teach me how to think properly like a mathematician. Thanks for the help

Terence Tao's "Analysis I". Title says "Analysis", but it really starts off with a rigorous treatment of sets and numbers.