Definition
Set Theory
Purpose
The purpose of set theory is to explore infinity using mathematical tools (1), acting as a universal language of Mathematics (2), and being the “hardware” of Mathematics (3).
- Exploring infinity: The crucial knowledge of the set theory is that there are different “sizes” of infinite sets.
- Universal language of Mathematics: All mathematical objects can be express by pure and hereditary set.
- Hardware of Mathematics: There are questions in “naive” Mathematics, that cannot be solved using the common tools, which are fundamentally related to set theory. Examples: Continuity Hypothesis, Whitehead Problem