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" )
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" )
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 $B$.