Re: infinity
- From: Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx>
- Date: Tue, 6 Sep 2005 14:21:11 -0400
imaginatorium@xxxxxxxxxxxxx said:
> Tony Orlow (aeo6) wrote:
> > imaginatorium@xxxxxxxxxxxxx said:
> > >
> > > Tony Orlow (aeo6) wrote:
> > > > Randy Poe said:
> > > <snip>
> > > > > Let me see if I have this "range" thing straight.
> > > > >
> > > > > 1. The range of the natural numbers is N. It's half of 2N.
> > > > The size of set of natural numbers is a natural unit infinity to use, but one
> > > > can have a double set, depending on one's construction.
> > > > > 2. But N is not the largest natural. N+1, N+2, ..., 2N, 2N+1, 2N+2
> > > > > are all in the naturals.
> > > > They are all whole numbers relative to the N under investigation.
> > > > > 3. The range of a set is the maximum difference between elements,
> > > > > so there are no elements of the natural numbers farther apart than
> > > > > N.
> > > > not in the basic set of natural numbers.
> > > > > 4. There is no maximum element of the naturals, so there is no
> > > > > maximum difference between elements.
> > >
> > > > But, if all elements are declared to be finite, no difference between them can
> > > > ever be infinite, so the maximum difference in the set is some finite value.
> > >
> > > Uh, so if you're counting these natural numbers with a ditty, the
> > > ditty, which (I _think_ we agree) need never stop, stops at this last
> > > mentioned finite value? This maximum difference of course might be the
> > > difference between 0 and the largest natural, and the nonexistence of
> > > this largest natural doesn't impair its functioning to stop the
> > > unstoppable ditty?
> > >
> > > This will never end.
> > >
> > > Brian Chandler
> > > http://imaginatorium.org
> > >
> > >
> > (sigh) Did you read what I wrote above? Forget your ditty. Sing it on the way
> > to the fair. My statement is clear. You say all elements are finite. Which do
> > you disagree with?
> >
> > 1) The difference between numbers A and B is abs(A-B)
>
> Sounds right.
>
> > 2) For finite A and B, abs(A-B) is finite.
>
> Sounds right.
>
> > 3) If all elements are finite, then any two of them is finite.
>
> No. Any two of them _are_ finite.
>
> > 4) If a number is finite, then it is not infinite.
>
> I don't know that I can agree with *your* statement of this, since you
> have never clearly defined what you mean by either term. In the
> mathematical statement that looks like the same string of words (ah,
> yes, which I see you fervently believe is what you are talking about)
> this is true, yes.
>
> > I can't imagine WHICH of these you could possibly argue with. Which is it?
>
> None, evidently. How about your next one, which will be something like:
>
> 5) Since for any pair of numbers you give me, I can give you a (finite)
> number larger than the difference between them, it follows [joke, Tony,
> OK?] that you can give a (finite) number larger than the difference
> between any pair of numbers I give you.
No, I cannot give any finite number that is larger than all finite numbers, but
I CAN say that any infinite number is larger than any finite number, and that
if you restrict your set to finite numbers, then there cannot be any infinite
numbers in it. Since all numbers are finite, the difference between any pair of
numbers is finite, and therefore there can be no infinite difference, and the
range of the set is finite.
>
> Brian Chandler
> http://imaginatorium.org
>
> **** Sorry about the finger trouble above !! ****
>
>
--
Smiles,
Tony
.
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