In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> On 1 Mrz., 23:51, William Hughes <wpihug...@gmail.com> wrote: > > > > The argument is not only time. > > > > m can change even though the time does not ? > > The maximum depends on the personal environment, the capability to > abbreviate numbers, the wish to do so, and many more factors. It > invents relativity into mathematics.
So that in WM's world there is a largest natural number whose value is variable and dependent on many factors, so that it may sometimes be increasing and sometimes decreasing. > > > > > But in general your description is > > > acceptable. > > > > > So what is your true opinion about this potential infinity which, > > > contrary to finished infinity, is not self-contradictory and allows > > > for all calculations required in analysis?
In the world of the majority, it is your potential infiniteness, not our actual infiniteness, that is self contradictory.
In our world every natural is required to have a successor, whereas in WM's world there must always be a natural not having any successor, though no one can say which one it is. > > > > I > > "Potential infinity" does not differ in any > > essential way from "finished infinity". > > The language changes a bit, and at times you need more words > > but the behaviour is the same. > > > > E.g > > > > With finished infinity you do not have a largest > > natural > > > > With potential infinity you do not have a largest > > non-variable natural > > > > With finished infinity there is no line of L > > that contains every FIS of d. > > But there are all FIS of d, which must be in infinitely many different > lines of the complete list.
if there are all of them, and each one has a successor, which it does, then there cannot be any last one. > > This is a contradiction, because the list, by definition cannot > fulfill this requirement.
It can, and does, everywhere outside Wolkenmuekenheim.
It is only inside such anti-mathematical places as Wolkenmuekenheim that one can have endless sequences with two ends. > > Why do you refuse to consider this simple fact?
It is certainly simple but only in the sense of simple-minded. > > > > With potential infinity there is no line of L > > that has a non-variable index and contains > > every FIS of d > > > > With finished infinity there are no balls > > in the vase. > > And we have a contradiction with analysis. Compare "The Paradox of > Tristram Shandy", PlanetMathOrg (2012)
Only fools like WM ever expect Tristam to finish recording his whole life. >
> > Two proofs against actual infinity. In addition there is the Binary > Tree which has not more than infinitely (aleph_0) paths that can be > distinguished even by infinite strings (with aleph_0 bits each).
Which only proves WM's incompetence at understanding what constitutes a proof.
If one could list all such binary strings, one could "distinguish" each path with a different string, and vice versa, because there is an easy bijection between their two sets, but listing all such strings is as impossible as listing all those paths.
But the set of all such paths has uncountably many paths that one will never be able to list. --