Quote:
Originally Posted by whswhs
Long ago, when I was taking real analysis, I asked my instructor why Cantor's argument didn't apply equally to whole numbers. He answered that rational numbers, in decimal representation, could have an infinite number of digits, but whole numbers could not.
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The issue isn't precisely infinite
digits, the issue is infinite
information content. If you limit yourself to real numbers that can be expressed by a finite equation, you wind up with a set that is no larger than the set of whole numbers.