Re: Cardinality of Real Numbers
- From: Robert Low <mtx014@xxxxxxxxxxxxxx>
- Date: Sun, 28 Aug 2005 19:54:26 +0100
jswimr3@xxxxxxxxx wrote:
I've been thinking about cardinality proofs lately, and I've run into something that's been bothering me. I thought of what seems like a mapping from the set of integers to the set of real numbers. Now, of course, this can't exist, so there must be something wrong with my mapping, but I can't see what it is.
The mapping works like this: for each integer, map it onto all the reals you can get by putting a decimal point anywhere in it. For example, 123 would map to:
This gives you all the reals that can be represented by a finite decimal expansion. You'll note that you never get the decimal expansion of 1/3 by doing this, since there is no integer consisting of infinitely many 3's. .
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- Cardinality of Real Numbers
- From: jswimr3
- Cardinality of Real Numbers
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