Re: Cantorian pseudomathematics

In article <1137629386.787934.98420@xxxxxxxxxxxxxxxxxxxxxxxxxxxx> "david petry" <david_lawrence_petry@xxxxxxxxx> writes:
> > That seems a bit like cheating. What do you mean by "we can show
> > that..."? How do we /know/ that there isn't some n where the next prime
> > after p_n doesn't appear until (p_n)^n + 11?
>
> It's a direct and easy consequence of Euclid's method of proof. Recall
> that he showed that for any set of primes, the product of all those
> primes plus one is either a prime or a product of primes not in the
> set.
....
> To say that there is no largest prime is not a falsifiable assertion,
> and hence it must be considered to be slightly vague.

It's a direct and easy consequence of Euclid's method of proof. So why
do you allow that above but not here? What is the subtle distinction?

How about: the non-trivial zeros of the Riemann zeta function have all
a real part 1/2. I would say that is a falsifiable assertion, but
"weakly" falsifiable in your current terminology.

How about the assertion pi(x) < Li(x)? It appears to be at least
"weakly" falsifiable. Should we allow to let such a statement stand
until it is falsified by computation? In that case it is a theorem,
it can *not* be falsified by computation, regardless the size of the
computer you are going to use. On the other hand, there are other
theorems that show it to be false, and I think you are of the opinion
that those other theorems are "rather vague". On what grounds?
Indeed such question are not interesting for the physicist, but they
are *very* interesting for many mathematicians.

You must really rid yourself of the idea that mathematics is only
part of physics. There is quite a bit of applied mathematics that
has really *nothing* to do with physics.
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