Date: Jan 27, 2013 1:21 PM Author: Jesse F. Hughes Subject: Re: ZFC and God WM <mueckenh@rz.fh-augsburg.de> writes:

> On 27 Jan., 18:44, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:

>

>> 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. Can't you understand? All natural numbers are finite.

> Why the heck should I define a single k?

Because, of course, you accepted the following definition:

Let x be a real number in [0,1]. We say that x has a terminating

decimal representation iff there is a natural number k and a

function f:{1,...,k} -> {0,...,9} such that

x = sum_i=1^k f(i) * 10^-i.

Thus, if you claim that 0.777... has a terminating representation,

then you must show that there is a natural number k and a function f

as above such that

0.777... = sum_i=1^k f(i) * 10^-i.

Else, you have no cause to claim that 0.777... has a terminating

decimal representation.

>> > 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?

>

>> 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.

Er, no.

The definition that you agreed to is reproduced above. You have to

show that the definition above is actually satisfied, i.e., that there

is a natural number k and a function f satisfying the appropriate

conditions.

You've done no such thing.

Frankly, I'm a bit stunned that you're arguing that 7/9 has a

terminating decimal representation, but as long as you're claiming so,

then you need to stick to the definition we've agreed on.

--

"Being who I am, I know that's a solution that will run in polynomial

time, but for the rest of you, it will take a while to figure that out

and know why [...But] it's the same principle that makes n! such a

rapidly growing number." James S. Harris solves Traveling Salesman