"In elementary set theory, Cantor's theorem states that, for any set A, the set of all subsets of A (the power set of A) has a strictly greater cardinality than A itself. For finite sets, . . . . But the theorem is true of infinite sets as well. In particular, the power set of a countably infinite set is uncountably infinite."5

   In the preceding section it was shown that the CH cannot exist in Tspace. But part of Cantor's Theorem can and does exist in three dimensional reality. The finite sets can contain material objects, or numbers or other symbols, which represent material objects. And the power set of those material objects will always be larger than the corresponding set.
   However, " . . . the power set of a countably infinite set is uncountably infinite," cannot exist in Tspace. It has already been shown that different sizes of infinity cannot exist in Tspace.

Paradoxes

   Paradoxes will forever remain in Ispace, but when they are solved, then possibly their solutions will translate to reality. All paradoxes can be solved, but some paradoxes are so radical that their solutions have very little resemblance to the original paradoxes. There are those who might consider these to be unsolvable paradoxes, even though they have been solved (an example of this will be shown later in the essay). Before paradoxes are solved, they cannot be translated to reality, because they are abstract contradictions which defy natural logic, and because material objects cannot be a contradiction to or of each other.    There are some references, which report that a paradox is:

   "A statement or proposition that seems self-contradictory or absurd but in reality expresses a possible truth."6

   But a paradox can only express a truth if it is solvable.

           
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