Re: Defining Natural Numbers

In article <1163858378.783276.84940@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,
<pradyumna.achar@xxxxxxxxx> wrote:
Hi all,
Given a set of symbols D = {0,1,2,3,4,5,6,7,8,9}, can we arrive at the
set of natural numbers without the use of any axioms ?

You can give an arbitrary characterization of the strings
which represent natural numbers (essentially a Backus
normal form), but you cannot deduce any properties, nor
need these strings have the properties one customarily
associates with this representation without axioms.

--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@xxxxxxxxxxxxxxx Phone: (765)494-6054 FAX: (765)494-0558
.

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