Many thanks, it's more than enough for me to dig around. > while the authors of mathematics texts have preferred to present systems of axioms like they would h

Many thanks, it's more than enough for me to dig around. > while the authors of mathematics texts have preferred to present systems of axioms like they would have been the result of random choices This is a frustrating situation, and a source of confusion in my experience, for example when we jump from the high-school "column of numbers" definition of vectors to the "element of a vector space" one. Or, how confusing the axioms for topologies are.