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Finite Implies Discrete; Not The Other Way Around.

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Posted by Paul R. Martin on April 28, 2001 00:42:45 UTC

Hi Alex,

It's even a little stronger than that. If numbers are finite, and bounded, then they must be discrete. That is, if there is a largest number, say N, then there is a smallest non-zero number which is 1/N. That forces numbers to be discrete.

If the numbers are not bounded, then you wouldn't necessarily have a smallest number and you could have a continuous number continuum as usual.

If you only have discrete numbers, they could still be unbounded, and you could have an infinite number of numbers. The normal set of integers is such a set of discrete but infinite numbers.

Warm regards,

Paul

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