Virgil
Posts:
4,674
Registered:
1/6/11
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Re: ZFC and God
Posted:
Jan 27, 2013 4:42 PM
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In article
<364860fe-77b9-4673-a29b-71c565afdd4c@u20g2000yqo.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:
> On 27 Jan., 18:44, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:
>
> >
> > > 0.7 is terminating.
> > > if 0.777...777 with n digits is terminating, then also 0.777...7777
> > > with n+1 digits is terminating. Therefore there is no upper limit for
> > > the number of digits in a terminating decimal. This fact is usually
> > > denoted by "infinite" and abbreviated by "...".
> >
> > Are you suggesting that 0.777... is *both* an infinite and terminating
> > expansion?
>
> In my opinion infinite has only one meaning, namely potenial infinity.
You opinion is of no value outside Wolkenmuekenheim .
> The set N is potentially infinite. There is no upper threshold
> although every FISON is finite. - And there is nothing else.
>
> By the AxInf we get a second infinity, namely a set N that has A
> elements, where for every n in N: A > n.
ONE measure of the finiteness/infiniteness of a set S is determined by
whether it can be injected to a proper subset of itself.
Sets like {1}, and {1,2}, and {1,2,...,n} cannot be injected to any
proper subsets of themselves, and sets which cannot be we call "finite".
However sets like |N CAN be injected into some of their proper subsets,
for example n -> n+1 injects |N to {2,3,4,...} which is a proper subset
of |N. Such sets are called "not finite", or more briefly, "infinite".
In standard mathematics "injectability to some proper subset" and
"non-injectability to any proper subset" are too awkward, s we replace
them with "infinite" and "finite" respectively.
We also note that one can prove that from the above definitions of
finiteness and infiniteness of sets one can show that
Set S is infinite if and only if her is an injection from |N to S.
But note that the existence of a set |N is not needed to definie
finiteness versus infiniteness of sets.
>
> If someone believes that this axiom is better than the axiom that
> there are 10 different naturals with sum 10, then he should try to
> find evidence. Hitherto I have not seen eveidence provided by you that
> AxInf would be useful or required.
>
> > Anyway, you haven't proved that there is a function
> >
> > f:{1,...,k} -> {0,...,9}
> >
> > as required by *your* definition of terminating decimal, so you have
> > not shown that 0.777... is a terminating decimal.
>
> You are wrong.
Perhaps in Wolkenmuekenheim, but nowhere else.
> Can't you understand? All natural numbers are finite.
> Why the heck should I define a single k?
Unless you can sow that a last k exists, you lose!
> >
> > > Note, there is another meaning of infinite, namely "actually
> > > infinite". Those who adhere to that notion *in mathematics* should
> > > show that it differs from "potentially infinite" *in mathematics*,
> > > i.e., expressible by digits.
> >
> > Well, I don't understand why anyone would wish to show that.
>
> Perhaps in order to show that matheology is not complete nonsense?
Comparing what WM calls our matheology and I call his WMytheology, I
find far less senses and more foolishness in WM's WMYTHEOLOGY.
>
> > But,
> > regardless, this is beside the point. I'm asking for a proof that
> > 0.777... is terminating according to the definition of terminating
> > that you agreed to.
>
> I did this in my last posting. Please look it up there. Well as I have
> it just at hand, here it is again:
> 0.7 is terminating.
> if 0.777...777 with n digits is terminating, then also 0.777...7777
> with n+1 digits is terminating. Therefore there is no upper limit for
> the number of digits in a terminating decimal. This is written as
> 0.777...
>
> This is the definition that I agreed to.
Then, according to WM, a terminating decimal need not have a last digit,
and can thus be represented s an infinite series..
ONe wonders how WM would define a non-terminating decimal;
>
> Regards, WM
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