Re: [PrimeNumbers] Pi(x)....4.....
- On Saturday 11 December 2004 02:30, you wrote:
> hiI guess now we have full proof that you are, indeed, a crackpot.
> i sead that becase the theory is realeted to phisics.so u are right.
Mathematics doesn't need physics to survive. At best one can use physical
concepts to motivate their work, but once a proper mathematical definition is
given, it should be possible to demonstrate it using mathematical tools
alone. Otherwise that `theory' is built on very shaky ground.
Anyway, now that you have shown the true nature of your `work', I consider the
thread closed and will no longer waste my time on it. Go ahead and clog your
festival with `publications' about crackpot theories all you want.
> but some times we can not proof some thing .we only define a difinition.No. Euclidean geometry relies on the fifth postulate (through a point P passes
> then some body may accept that and others may not.for example about
> Non-Euclidean geometry ....
a single line that is parallel to another given line). Lobatchevsky asked
``hmm, what happens if I replace `a single line' with `infinite lines'?'' and
gave us hyperbolical geometry. Riemann asked ``hmm, what happens if I replace
`a single line' with `no lines'?'' and gave us elliptical geometry. Whether
you accept or not Euclid's fifth postulate, or choose to replace it with
Lobatchevsky's or Riemann's version, is beside the point -- their results are
consistent with their assumptions and can't be debated.
To see the point, let's postulate that some set S can be associated with two
operations + and *, such that
1. +,* are associative;
2. + is commutative;
3. * distributes over +;
4. For each element of the set, there exist inverse elements wrt +;
5. There exists an identity 0 wrt +.
Then I'll refer to (S,+,*) as a `ring'. Results about `rings' abound, just
like the results of Riemannian geometry. Now I'll postulate that there exists
an identity 1 wrt *, and call this new entity a `unit ring'. I can prove
results about `unit rings' that couldn't be proved about `rings' if I accept
this new postulate. Now if I postulate that the operation * is also
commutative, that there exists an identity 1 wrt *, and that this ring has no
divisors of zero, then I'll refer to my new entity where both postulates are
valid as an `integral domain'. Results about `integral domains' abound,
complementing and extending the results about `rings' and `unit rings'. Now
if I also assume the existence of multiplicative inverses, then I'll refer to
this new entity as a `field', which has an even stronger body of results
complementing the remaining results.
Now, there exist many algebraic entities that satisfies some of these
postulates but not others. So there's no point in arguing whether Euclidean
geometry is the `right' geometry or not -- it's a great tool to describe the
geometry of flat spaces, but it's useless to describe the geometry of a
sphere, for instance.
Sorry for the overly long diatribe, but some crackpot needed an intro to
[Non-text portions of this message have been removed]