give an example (if possible) or a counterexample (if not possible):
a set U with |P(U)|= |Q|
Q= rational numbers.

Question

give an example (if possible) or a counterexample (if not possible):
a set U with |P(U)|= |Q| 
Q= rational numbers.

slaaibak · Answer

Just a quick question:  Does the || refer to cardinality?

also, what is the notation of P(U)? is P(U) a function?

If it's a function, and it's for example the identity function P(x) = x, then U = Q should suffice.  But I don't know much about set theory

anonymous · Answer

yes, || refers to cardinality. P(U) is the powerset of U. what im thinking is that since P(U) is uncountable and  Q is countably infinite, they cannot be equal but im not sure if im right.

anonymous · Answer

and can't find a counter example. im going with definitions.

slaaibak · Answer

I just read that |X| < |P(X)|

so the counterexample would be that U = Q

anonymous · Answer

off course! thank you!

slaaibak · Answer

no problem, happy to help.