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BUT - it can be shown that for every number N in Sets A and B, between 1 and 2, there exists a number (N+1), in Set B, located between 2 and 3.

THEREFORE, while both sets of numbers are infinite, inductive reasoning tells us that Set B should be twice as large as Set A, even though both are innumerable.

Oh I totally understand that. But I still think they're equivalent. You can neither halve nor double infinity. There are not portions of infinity, nor ranges of infinity.

How many angels can dance on the head of a pin?

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