what do areas of math like Set Theory bring us?
In: Mathematics
Set theory is the first common foundation of math.
Before set theory, there are no common foundation. Arithmetic and number theory follow their own rule. Analysis follow their own rule. Geometry follow their own rule. There are no consistency, there is no guarantee that they’re compatible with each other.
Set theory allow you to do that. When you use set theory as foundation, everything is made of set, and follow the same axioms. And your mathematical objects can be defined explicitly, for example “a natural number is a set that satisfies property …”.
After set theory, other foundations had been suggested, which had improvement over set theory. For example, they might be easier for computational purposes, or more suitable for computer proof-checking, and these had uses in bug-free programming.
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