3
$\begingroup$

Can every set have a power set ?

Does there exist a set A such that there always is a surjection of A onto B , where B is any arbitrary set?

(note that positive answers to both the questions lead to a contradiction by "Cantor's theorem" )

  • 0
    @ Martin Sleziak: What I meant to say is that positive answers to both the questions 'together' lead to a contradiction , as Brian Scott already has said , still sorry for the lack of clarification.2012-10-08

1 Answers 1

2

One of the axioms of ZF set theory is that every set has a power set. There is no set $A$ such that for each set $B$ there is a surjection of $A$ onto $B$.