On 3/22/2013 5:14 AM, WM wrote: > On 22 Mrz., 10:49, fom <fomJ...@nyms.net> wrote: >> On 3/22/2013 4:13 AM, WM wrote: >> >>> On 22 Mrz., 09:54, Virgil <vir...@ligriv.com> wrote: >>>> On 3/22/2013 1:38 AM, WM wrote: >> >>>>> This proves that we can remove all finite lines from the >>>>> list without changing the contents of the remaining list. And this is >>>>> remarkable, isn't it? >> >>>> Since WM also claims that all the lines of that list are finite lines, >>>> WM is now claiming one can trow out the entire contents of a list and >>>> still have the entire original list in place. >> >>> That is a consequence of the completed infinity of set theory. >> >> He is referring to your claims > > I know. They are a consequence of finihed infinity. >> >> >>>> Unfortunately, as in the above claim, what WM claims to be the case >> >>> can be proven by induction that holds for every finite line. >>> Every number that belongs to line n belongs to the next lines too. >> >> It should be observed, once again, that the most WM is ever referring >> to with statements like this is the form of the domain for an >> induction rather than any true use of inductive proof. > > True use of inductive proof has been fonuded by Fermat without any > reference to domain. Your "true use" refers to "the only method you > have been taught".
I missed this one.
Once again, WM is turning back to a time before axiomatic mathematics.
He just posted 228 in which it is acceptable to have the pure imaginary unit as a number.
What then is a number? If there are different kinds of numbers, what distinguishes numbers from non-numbers? What do we call a collection of given numbers that are the same type? Would that be a number system? What is the criterion for calling an arbitrary collection of objects a number system? Would that be an arithmetical calculus?
Why should any arbitrary collection of objects with an arithmetical calculus not be called a number system?