On 3/17/2013 2:57 PM, Virgil wrote: > In article > <email@example.com>, > WM <firstname.lastname@example.org> 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. >
And, necessary to the proof of an algebraically closed field.
But when one 'knows' such things 'by reality' there is no need of definition or proof.