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You have both decided to give infinity a meaning that it hasn't got.
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So the great mathematicians of the 19th century such as Cantor etc. were incorrect to give infinity a meaning.
http://en.wikipedia.org/wiki/Uncountable_set
http://en.wikipedia.org/wiki/Countable_set
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A standard human mind trait that must try to explain something that can't be explained. To say that infinity is smaller than smallest or larger than largest is still giving it a meaning that is not infinity. Once the mind can understand infinity most of the other bounding consepts we have will start to have a new meaning.
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It's not the case.
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Some sets are infinite; these sets have more than n elements for any integer n. For example, the set of natural numbers, denotable by , has infinitely many elements, and we cannot use any normal number to give its size. Nonetheless, it turns out that infinite sets do have a well-defined notion of size (or more properly, of cardinality, which is the technical term for the number of elements in a set), and not all infinite sets have the same cardinality.
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Regards
Steven