If one were to do a bottom up study of math how would it go?(adsbygoogle = window.adsbygoogle || []).push({});

Set theory

.

.

.

?

Is set theory the most fundamental, or does it build on the axioms of some other ideas?

Also, in what section of mathematics is the concept of vectors established? What about "euclidean space" or "other space" established?

Are things like exponentiation arbitrarily defined or is there something more to it that is developed somewhere?

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# Hierarchy of math

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