Re: Coding of ordered pairs
- From: William Hughes <wpihughes@xxxxxxxxxxx>
- Date: Wed, 05 Sep 2007 09:31:44 -0700
On Sep 5, 8:23 am, Han de Bruijn <Han.deBru...@xxxxxxxxxxxxxx> wrote:
Quoted without permission from:
http://www2.informatik.hu-berlin.de/~grohe/pub/cheflugro05.pdf
Here, < , > : N x N -> N
STOP
You claim that the set of naturals does not exist, nor
does a function whose domain is the set of naturals exist.
Despite this you want to make sensible remarks about
such a function.
is any simple coding of ordered pairs
of natural numbers by natural numbers
such that <i,j> <= (1 + max{i,j})^2 and <0,0> = 0.
But I don't quite understand how such a "simple coding" can be done.
Suppose that we don't know beforehand whether there is a maximum element
in {i,j}
You have a completely different view of mathematics and should
ignore this "simple coding".
how can we devise a mapping "like" the above, such that (i,j)
can always be reconstructed, as an ordered pair, from a single natural
number <i,j> ?
Well, you would have to start with a definition of the natural numbers
such that
we don't know beforehand whether there is a maximum element in
{i,j}
makes sense. Then you would have to find someone who finds this
definition interesting.
- William Hughes
.
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