Virgil
Posts:
8,833
Registered:
1/6/11


Re: ZFC and God
Posted:
Jan 27, 2013 4:42 PM


In article <364860fe77b94673a29b71c565afdd4c@u20g2000yqo.googlegroups.com>, WM <mueckenh@rz.fhaugsburg.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 "noninjectability 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 nonterminating decimal; > > Regards, WM 

