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4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / c. Basic theorems of ST

[useful simple theorems derived within set theory]

4 ideas
The ordered pairs <x,y> can be reduced to the class of sets of the form {{x},{x,y}} [Dummett]
Cantor proved that all sets have more subsets than they have members [Bostock]
Cantor's Theorem: for any set x, its power set P(x) has more members than x [Hart,WD]
The empty set Φ is a subset of every set (including itself) [Priest,G]