In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> Am Donnerstag, 12. Dezember 2013 20:07:12 UTC+1 schrieb Zeit Geist: > > > > > by digits that have a finite index. Please don't forget that. >
> Matheology usually claims the handwaving "infinite sequence" and tries to > make us forget that even in such an infinite sequence every digit has a > finite index.
Actually the mathematics that WM insults so freely is quite aware that each term in an infinite sequence has a finite index, bu tWm seems to forget that those seuqnces are called infinite because they are infinite. > > Only that is required for my proof.
Wm speaks of having proofs but has yet to produce anything that qualifies as one anywhere outside of his wild weird world of WMytheology.
> > > > But, there are infinitely many of those finite indices. > > And you think infinitely many finite indices will make us forget that each > one is finite and has infinitely many duplicates in the list? I know this > "argument". Apparenly not well enough.
> I don't know of infinite indices.
But the amount that WM does not know Is infintie. > > > > > > > > You claim, For All x e N, phi(x) is True; thus phi(N) is true. > > No, I do not. I claim that phi(x) is true for every x. Nothing else.
WM also claims that every x does not include all x's.
One wonders where the gap betwee every x and all x's exists in WM's wild weird world of WMytheology, since it clearly does not exist anywhere else.
> > > > Phi(x) here is "There exists a Rational Number of length x, which is Equal > > to d.". > > I am not at all falling into that trap!
Then you concede that there is no rational number of any length which is equal to d, as we have been pointing out all along. > > > > > > > > > And if you acknowledge that d is nothing more than its digits, then > > > > > there are infinitely many rational identical with d. > > > > > > > > > > > But it is more. It is a certain arrangement of digits. > > > > > > > > > > Yes, but this certain arrangement is never visible before the last digit.
For each d_n, enough of d is visible to prove it different from d_n.
All one needs to distinguish it from any d_n is to know d's nth digit.
> > But we know: For All n e N, the n-th Decimal Digit of 1/9 is "1". > > You know it from the finite formula.
Sometimes, as here, a finite formula applies equally well to an actual infinity of individual cases.
> > > > If that does Not mean 1/9 is "defined by digits", please explain. > > Simple: You cannot conclude from any given sequence of digits how it will be > continued.
You can if you are given in one statement every possible finite sequence.
> > > > > > > > Meaningless and Garbled. > > > > > > > > > > I am sure than many understand it
The only one who even claims to unsderstand WM'S WILD WEIRD WORLD OF WMYTHEOLOGY is WM.
> > No, you just wrong. > > > > It is you Philosophical Block. > > You see your block activated above: "But, there are infinitely many of those > finite indices." What should that be good for? Infinitely many failures will > gain a success?
Those infinitely many finite indices are only failures in WMytheology, because they are being asked by WM to do what they are not supposed to be doing. But the collection of all of them, which is available everywhere OUTSIDE of WM's wild weird world of WMytheology, can do things that WM seems unable to understand. > > > > You reject the Existence of an Infinite Set on Purely Philosiphical > > Grounds. > > I do not reject it at all. I assume that it exists.
That is a change.
Previously WM claimed that no such things as an infinite sets could ever exist.
Perhaps WM can learn! > > > > > If you have a Formal (Contradiction free) Definition of "Constructible", > > then there is No such 1:1 Correspondence. > > I need no definition other tham: A constructible number is defined by a > finite definition.
that doe not define "conatructable".
> In set theory subset cannot have larger cardinality than > the super set.
But the powser set must alway have a larger cardinality that the set it is constructed from. as if not ther wold have to ve a surjection from such a set to its own power set, which has bee proven impossible, at least imposible outside of WM's wild weird world of WMytheology.
> A subset of a countable set is countable,
But the power set of countable set need not be countabe, at least not unless the base set is finite.
Note that claiming that any set. power set or otherwise is countable, requires proof of a surjection from |N to that power set.
And no such surjection is possible between |N and its own power set. --