



 
Justin, It all comes down to what we consider to be the "size" of a set. We say a finite set has size n if it can be put into 11 correspondence with the set {1, 2, ..., n}. This idea can be extended to say that two sets have the same size if they can be put into 11 correspondence with each other. For instance, the set of all squares of integers has the same size as the set of positive integers because they can be put into 11 correspondence. This leads to the idea of sets being the same size as the integers, or the reals, or whatever. It turns out that no set, finite or infinite, can be put into 11 correspondence with its power set (the set of all subsets of the set). Therefore, if X is an infinite set, the power set of X is a "larger" infinite set. Since this process can be continued, there is no largest size of a set. Hope this helps. Justin, Many people had trouble with that idea when Cantor introduced it. RD  


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