Re: Epistemology 201: The Science of Science

stephen_at_nomail.com
Date: 02/14/05 

Date: 14 Feb 2005 20:00:00 GMT

In sci.math Tony Orlow (aeo6) <aeo6@cornell.edu> wrote:
: Yes, but that doesn't address whether there are any REALS that are not
: represented in a number-base system with infinite digits. Is there not a
: 1-1 correspondence between reals and rationals?

No. The rationals are countably infinite. The reals are not.

: Let's try this another way. It is obvious that there are an infinite
: number of rationals between any two integers. Are there an infintie
: number of reals between any two rationals, even though one can construct
: a rational that is arbitrarily close to any given real?

Yes, there are an uncountably infinite number of reals between any two
rationals, and there are a countably infinite number of rationals
between any two reals.

Stephen

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