Re: prime numbers and African artifact
Daniel Kian Mc Kiernan (dmckiern@weber.ucsd.edu)
Sun, 16 Jul 1995 19:04:39 0700
On 14 Jul 1995, Michael Jennings wrote:
] Daniel Kian Mc Kiernan <dmckiern@weber.ucsd.edu> 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.
Please, don't do battle with strawmen; it is wasteful of everyone's
time. I did =not= claim that one could engage in the sort of
transformation that =you= propose. I didn't give a =count= of how
many instantiations of "except one" (or an equivalent phrase) would
be required, nor did I bother to identify a particular =site=; I
only indicated that it would be required =somewhere= in either
system of expression. The reason that I didn't provide such details
is that there are more ways than one to do it. There =isn'at=,
however, a way to truly avoid doing it =somewhere=.
] 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.
You are confusing the =content= of mathematics with the =expression=
of mathematics, which is a beastly bad thing for a mathematician to
do. =All= of the theorems make sense if expressed in accordance
with the definitions of the terms. Naturally, if "prime" is defined
in one way, then the expressions have to be of one form; and if
"prime" is defined in another way, the expressions have to be of
another form.
It's always Dark. Light only hides the Darkness.
Daniel Kian Mc Kiernan (619) 535  0546
athanatos@UCSD.edu 132.239.147.2 <75013,676>
