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Are set theory functions sets too?

  1. Aug 6, 2015 #1
    I read somewhere that mathematical functions can be implemented as sets by making a set of ordered tuples <a,b> where a is a member of A and b is a member of B. That should create a function that goes from the domain A to the range B.

    But set theory has functions too, could they be sets too?

    For example the Power function would just be the set witht eh tuples <{},{{}}> and <{{}},{{}{{}}}> and so on. And the union and the pair function could be made into sets as well.

    So what I want to ask is can all functions in set theory be defined as sets themselves?
  2. jcsd
  3. Aug 6, 2015 #2
    Yes, if the domain of the function is a set. The power set function has as domain the class of all sets, this is not a set due to Russel's paradox. So the power set function can not be described as a set. Rather, it must be described as a logical formula.
  4. Aug 6, 2015 #3
    OK thanks!
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