##  [Cantor's Theorem](/cantors-theorem) 

  ##  [Cantor's Theorem](https://mathlogic.quantumdictionary.io/cantors-theorem-0) 

  

 [![Mathematics & Logic Dictionary](/sites/default/files/styles/large/public/2026-01/Mathematics%20%26%20Logic.png.webp?itok=UhtTRPnp)](/topic-specific-dictionaries/natural-formal-sciences/mathematics-logic)

- Natural & Formal Sciences -

**Mathematics & Logic Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The theorem that for any set S, the power set P(S) (the set of all subsets of S) has strictly greater cardinality than S itself; in particular there is no surjection from S onto P(S).