Date: Jan 27, 2013 4:42 PM Author: Virgil Subject: Re: ZFC and God 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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