Re: abundance of irrationals!)
From: Matt Gutting (tchrmatt_at_yahoo.com)
Date: 02/26/05
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Date: Fri, 25 Feb 2005 19:04:00 -0500
Jesse F. Hughes wrote:
> Matt Gutting <tchrmatt@yahoo.com> writes:
>
>
>>No, they recognized (even with Pythagoras and Euclid) that irrational
>>numbers (*not* proportions) had meaning; for example, that the irrational
>>number sqrt(2) has meaning as the length of the diagonal of the square
>>with side length 1.
>
>
> I don't think that Pythagoras or Euclid had any concept of irrational
> numbers, did they?
>
> They were interested in incommensurable *lengths* (and volumes, too, I
> guess), as far as I know, not numbers. We associate lengths (and
> volumes and so on) with numbers, but as far as I understand, they
> didn't do this.
>
Good point about the lengths. On the other hand, I don't know if their concept
of length was sufficiently distinct from their concept of number to allow them
separate formal definitions of the two. Unfortunately, I don't know enough
history of math to say one way or the other. (Running off to look at my "History
of Mathematics" books now)
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