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I'm new to this site and I'd like to begin my thread posting by asking about the foundations of mathematics. The more I learn math, the less I feel I know and it is getting a little depressing. I have two semesters of college level calculus under my belt (ending the year with Taylor and Maclaurin series), but now I want to learn about math from the ground up. I want to learn the axioms of mathematics, learn about number systems, and learn how to create and use math proofs. Can anyone suggest some books that could really help me learn more about math, starting from the beginning (the axioms)?