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> > There are many cases in mathematics where things are
> > known to exist but there may not be a procedure to find
> > them in finite time.
Dik T. Winter wrote:
> There are also many case in mathematics (before Cantor) where it is
> proven that something exists without even giving a procedure to find
> it (also when such a procedure could be given).
For example,
> The proof that given
> a finite set of primes there is also a larger one does *not* give any
> method how to find that prime; it just shows that there is one.
This is a bad example.
In the first place, There Is No Such Thing as "the" proof that
given a finite set of primes, there is also a larger one.
There are several ways to prove that, and -- in the second
place -- arguably THE MOST
simple and straightforward one, THE ONLY one that would be
ENTITLED to call itself "the" proof (if any were), is simply to
multiply
all the primes in the set and add 1 to the product, WHICH IS a
method. This sum is not guaranteed to be prime, but it was
so guaranteed under the assumptions of the problem (one of which was
that the finite set was all the primes there were).
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