Infinity and indefinite extensibility

From: David Cressey <dcressey_at_verizon.net>
Date: Sat, 20 May 2006 12:50:00 GMT
Message-ID: <YfEbg.223$J95.135_at_trndny05>

There is probably some standard terminolgy for what you are about to read. I don't know what that standard terminology is. Sorry about that.

I think it's worthwhile, in the discussion of infinite domains and finite state implementations, to distinguish between "infinite" and "indefinitely extensible".

For example, the familiar decimal place value notation system for natural numbers is indefinitely extensible. That is, there is no such thing as the largest natural number that the scheme can represent. If a number can be represented in decimal, its successor can be represented as well. And so on.

However, every number that can be written in decimal is finite. And every set of natural that has been formed by listing the elements is a finite set. And this will remain true until the twelth of never. (yuk, yuk).

You can't represent "infinity" with natural numbers, but there is no upper bound to the range of natural numbers.

It seems to me that this distinction would be revelant over in the "impossible database design" topic. Received on Sat May 20 2006 - 14:50:00 CEST