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Single Idea 13444

[filed under theme 4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / c. Basic theorems of ST ]

Full Idea

Cantor's Theorem says that for any set x, its power set P(x) has more members than x.

Gist of Idea

Cantor's Theorem: for any set x, its power set P(x) has more members than x

Source

report of George Cantor (works [1880]) by William D. Hart - The Evolution of Logic 1

Book Ref

Hart,W.D.: 'The Evolution of Logic' [CUP 2010], p.16

The 4 ideas with the same theme [useful simple theorems derived within set theory]:

13444 Cantor's Theorem: for any set x, its power set P(x) has more members than x [Cantor, by Hart,WD]
18098 Cantor proved that all sets have more subsets than they have members [Cantor, by Bostock]
10537 The ordered pairs <x,y> can be reduced to the class of sets of the form {{x},{x,y}} [Dummett]
9680 The empty set Φ is a subset of every set (including itself) [Priest,G]