"Most logical paradoxes are known to be invalid
arguments but are still valuable in promoting critical thinking."^{7}
Cantor's paradox arises from the following. Let there be an
infinite Universal Set of all Sets, U, which means this set contains
all sets, subsets, and power sets. U = {sets, subsets, power sets}.
Let the infinite power set be the Universal set's power set. Since
the power set is a set, then it must be contained within the
infinite Universal set, because the infinite Universal set contains
all sets. From this it can be concluded that the power set is less
than or equal to the Universal set. But Cantor's theorem
demonstrates that the power set is always larger than the set. And
herein lies the paradox. The infinite P(C) ≤ the infinite C. The
cardinality of the infinite power set is less than or equal to the
cardinality of the infinite Set of all Sets. But by Cantor's
theorem, P(C) ˃C. The cardinality of the power set is greater
than the cardinality of the set. And thus, the paradox. The power
set is larger than its set, but the power set is equal to or smaller
than its set.

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