Re: prime
- From: "Proginoskes" <CCHeckman@xxxxxxxxx>
- Date: 18 Apr 2006 23:54:24 -0700
Bill Dubuque wrote:
richard@xxxxxxxxxxxxxxx (Richard Tobin) writes:
Brainy <brainy@xxxxxxxxx> wrote:
It`s has been said that there are not existing negative Primes,
does anyone has a written formule which has proven this?
It's not a matter of proof, it's just a matter of definition.
If you include negative numbers as primes, then you will often (at
least when talking about the integers) find yourself needing a term
like "positive primes", for example to state the unique factorisation
theorem. Including 1 as a prime is similarly inconvenient.
But there are some contexts where it is convenient to consider
-1 as a prime, as John Conway argues in his award-winning book
The Sensual (Quadratic) Form. He has defended this definition
online in various forums, e.g. see [1].
In certain contexts it may prove more convenient to work with
definitions that are perturbations of the standard ones. [...]
For instance, if you claim to have proven a result, and your proof is
clearly wrong, you can argue that the definition of something is wrong.
A poster whose name rhymes with Hames Jarris has recently used this
tactic, arguing that the square root function is not well-defined. Note
that if you use this maneuver, you will be labelled as a crank.
--- Christopher Heckman
.
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