In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> On 17 Mrz., 00:25, Virgil <vir...@ligriv.com> wrote: > > > > > Can WM provide any definition for natural numberss which doe not state, > > > > or at least imply, that every natural must have a successor natural? > > > > > Numbers are creations of the mind. Without minds there are no numbers. > > > > Which is not a relevant answer. > > By definition of a matheologian.
Which is a non-response to my original question: Can WM provide any definition for natural numberss which doe not state, or at least imply, that every natural must have a successor natural?
WM's failure to respond positively I take as a "no" answer. > > > > > > Can WM provide an definition for natural numbers which doe not state, > > or at least imply, that every natural must have a successor natural? > > It is always stated or at least implicitly assumed in classical > mathematics that we are able to add 1. In reality this is an erroneous > assumption as has been shown in MatheRealism.
Unless you can produce such a natural, which even in your alleged "mathrealism" you have not done, your claim is, as always, unfounded. > > > > > you are not able to write aleph_0 digits of a real numbers like 1/9. > > > > So what? There are lot of things in mathematics one cannot do, but that > > should not keep us from doing what we can do, the way you would limit us. > > But the claim of matheology is that all digits exist and can be > determined - for instance all digits of pi.
I do not make the claim that all the digits of the number pi can be found, but I do claim that the number pi has a definition, as do infinitely many other reals whose exact decimal representations cannot be found.
E. g., the square roots of each of the infinitely many primes are all defined, though none can be given exactly as decimals.
WM has frequently claimed that HIS mapping from the set of all infinite binary sequences to the set of paths of a CIBT is a linear mapping.
In order to show that such a mapping is a linear mapping, WM would first have to show that the set of all binary sequences is a linear space (which he has not done and apparently cannot do) and that the set of paths of a CIBT is also a vector space (which he also has not done and apparently cannot do) and then show that his mapping, say f, satisfies the linearity requirement that f(ax + by) = af(x) + bf(y), where a and b are arbitrary members of the field of scalars and x and y and f(x) and f(y) are arbitrary members of suitable linear spaces.
While this is possible, and fairly trivial for a competent mathematician to do, WM has not yet been able to do it.