Re: Does anyone have a purely scientific objection to evolution?

"On Tue, 03 Jun 2008 11:38:24 -0500, in article
<g23s27$ceq$1@xxxxxxxxxxxxxxxxxxxxxxx>, Don Cates stated..."



Rupert Morrish wrote:
r norman wrote:
On Mon, 02 Jun 2008 12:54:12 -0400, noshellswill
<noshellswill@xxxxxxxxx> wrote:

On Sun, 01 Jun 2008 13:22:46 -0400, r norman wrote:

On Sun, 01 Jun 2008 08:10:35 -0400, noshellswill
<noshellswill@xxxxxxxxx> wrote:

On Sat, 31 May 2008 02:16:24 +0000, John McKendry wrote:

On Fri, 30 May 2008 15:43:46 -0400, noshellswill wrote:

On Fri, 30 May 2008 12:37:44 -0400, r norman wrote:

On Fri, 30 May 2008 12:27:09 -0400, noshellswill
<noshellswill@xxxxxxxxx> wrote:

On Fri, 30 May 2008 08:43:04 -0700, chris thompson wrote:


It's a quibble -- but a useful one -- to note that NOT ALL sets
are
complete under addition. That is you add two numbers and expect
the SUM
to exist within that set. But it doesn't need to ! Surprise
surprise. A classic example is the <space> of rational numbers
which contains
sums approaching an IRRATIONAL number and thus not "in the space".

x + y = ?


What nonsense. The rational numbers are closed under addition.
Period.
The fact that you can find an infinite series of rationals whose
limit is not rational is an entirely different issue. That simply
means the set is not closed in a topological sense.
rn:

Granting my point - in response to CT - you would do better to just
grovel.

nss
******
Grovel? When your "point" was a simple error? You said "you add
two numbers and expect the sum to exist within that set", and then
you
said that the rationals don't have that property. The rationals do
have that property. There's no two ways to interpret it; what you
said is wrong. Your hand-waving in the direction of limits of
sequences
suggests that you intended to say something else, but you didn't
manage it. In mathematics, you don't get credit for what you meant
to say.
Picky picky ... you have a problem with "limits" ? Surely you can
extend
a bit, eh? I believe you are avoiding the issue posed by the
original post
and my response.

Picky picky, indeed! What you wrote is " NOT ALL sets are complete
under addition. That is you add two numbers and expect the SUM to
exist within that set. But it doesn't need to !" The set of rational
numbers IS complete under addition. You are wrong, plain and simple.
Your comment about sequences has absolutely nothing to do with sums.

It doesn't matter what the original post was if your response to it is
wrong.

' A classic example is the <space> of rational numbers which contains
sums approaching an IRRATIONAL number and thus not "in the space". '

Nope. not wrong. But you editing of my post is not in good-faith.

You are weaseling unsuccessfully. The set of rational numbers
contains elements approaching an irrational number. The fact of
summation is totally irrelevant indicating you completely
misunderstand the phrase which I accurate quote: "complete under
summation". I also quote you correctly in writing "That is you add
two numbers and expect the SUM to exist within that set. But it
doesn't need to ! Surprise surprise." and then give rational numbers
as an example. The sum of rationals always does exist within that
set. The rationals are indeed complete under summation.

He's weaseling correctly ;) You're missing the distinction between sets
and spaces.

Well, no. *He* missed the distinction between 'sets' and 'spaces'. His
claimed "classic example" illustrating "you add two numbers and expect
the SUM to be within that set" was *not* such an example. It illustrates
something else entirely.

You have it right. I'd suggest looking at the Wikipedia article
"Closure (mathematics)" for some different ways in which the word
"closed" is used in mathematics.

But I'd also complain about confusing language like this:

A classic example is the <space> of rational numbers
which contains
sums approaching an IRRATIONAL number and thus not "in the space".


"Sums approaching an irrational number"? What is that supposed to
mean? Yes, there are infinite sequences of rational numbers which
have a limit which is irrational. Yes, those can be expressed as
infinite sequences of sums of rational numbers (for the trivial
reason that every rational number can be expressed as a sum of
rational numbers); For example, the sequence of rational numbers
that has a limit of pi: 3, 3+1/10, 3+1/10+4/100, 3+1/10+4/100+1/1000,
and so on.




You're talking the set of rationals, which is indeed closed under
addition. The space of rational numbers with limit sums is, however,
open. Summing a finite series of rational numbers gives a rational
number, but the limit needn't be.

I'm not sure why he brought it up, other than to show off, but he's not
wrong.



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--
---Tom S.
"As scarce as truth is, the supply has always been in excess of the demand."
attributed to Josh Billings

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