Re: prime numbers and African artifact
Michael Jennings (M.J.Jennings@amtp.cam.ac.uk)
14 Jul 1995 13:12:07 GMT
In article <Pine.HPP.3.91.950713210709.20912Cfirstname.lastname@example.org>,
Daniel Kian Mc Kiernan <email@example.com> wrote:
>No one is calling the importance of the theorem into question. It
>is only insofar as how a definition of "prime" affects the felicity
>of expression that the theorem can here be brought into play. NOw,
>you didn't give a formal statement of the theorem, but nonetheless
>look at what you did say, and how you said it. It really comes down
>to nothing more than a question of where one sticks in "except one"
>(or the equivalent) in the expression.
No. That is not correct. My addition of 'except one' into
the fundamental theorem is _not_ the same thing as putting the
'except one' into your original definition. If it was, then
the theorem would remain true if we removed the 'except one' in
both cases. Looking at it another way, if what you are saying
is correct, excluding the 'except one' from the definition of
a prime number I gave in terms of the fundamental theorem of
arithmetic would lead to a set of prime numbers inclding one.
It does not do this. In this case, the fundamental theorem
of arithmetic (and consequently the definition) simply ceases
to make sense, as the idea of a 'unique decomposition' is lost.
The reason that one is not a prime number is because virtually
all theorems in mathematics based on prime numbers do not make sense
if we include it. What's more, they _cannot_ be made to make sense
if we include it.
Department of Applied Mathematics and Theoretical Physics
The University of Cambridge. firstname.lastname@example.org
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