Re: The rational number 5 and the real number 5
- From: William Elliot <marsh@xxxxxxxxxxxxxxxxxx>
- Date: Thu, 6 Mar 2008 02:48:42 -0800
On Thu, 6 Mar 2008 djrt20@xxxxxxxxxx wrote:
The real number 5 is the name we give to [(5,5,5,...)] if real numbersWhat makes sense is that there is an isomorphism between the rational
are defined to be equivalence classes of Cauchy sequences of
rationals. Maybe we would like to say that the real number 5 is equal
to the rational number 5. In what sense does it make sense to say
this, and is there anything wise to say here?
numbers and the subfield of the real rationals of the reals.
In otherword, the rationals embed into the reals.
Of course 5 the integer, 5/1 the rational and 5.0000....
the real are not equal until you embed the integers
into the rationals and the rationals into the reals.
Then it makes sense to define 5/1 as 5.000... and 5 as 5/1.
.
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