"Then assemble these possibilities into a well-defined set of ideas using mathematical concepts, language, and notation to form statements (axioms) that are taken to be true and built upon to form further axioms."
Think you should have said further *theorems there.
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"Then assemble these possibilities into a well-defined set of ideas using mathematical concepts, language, and notation to form statements (axioms) that are taken to be true and built upon to form further axioms."
Think you should have said further *theorems there.