Subject: Re: Diagonal Process
Date: Tue, 14 Jan 1997 19:20:25 -0500
From: Alex Bogomolny
> One will need to stop some
No, the problem is you can't even start writing sqrt(2) right to left. This is one problem in what you attempt to do. The second is that whatever you do you do dynamically. You write
> I can not figure out why this 1-1 correspondence
> should be broken just by adding digits to an infinite sequence.
you do not have a 1-1 correspondence to start with, not to talk of breaking one. It's not up to you to add or remove digits from the decimal expansion of a number. You have to consider a number as a whole. Otherwise, you can have two numbers that differ only in one digit some where a mile from the beginning. With your dynamic assigment of integers, for a long while you won't have any 1-1 correspondence. And you run into this trouble by just looking into two numbers. But there is an infinitude of such situations which should be dealt with simultaneously. This is another reason your dynamic process would not work.