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

On Tue, 03 Jun 2008 09:28:50 +0100, Ernest Major wrote:

In message <4844b055$0$14281$8d2e0cab@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,
Rupert Morrish <rupert@xxxxxxxxxxx> writes
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

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.

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.

It appears that he was equivocating (not making a distinction between)
sets and spaces, and also addition and summation, as he wrote "NOT ALL
sets are complete under addition. That is you add two numbers and expect
the SUM", and then offered summation within a space as a counterexample.
There are sets which are not closed under addition, e.g. the set of odd
integers, but the *set* of rational numbers isn't one.

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

The subtleties of higher algebra sometimes escape me (should it be
significant that he wrote complete rather than closed?), but it's not
clear to me that he was right.

EM:

I'm not so sure myself - having re_read the entire thread. I never
intended to "weasel" as that behavior is NEVER seen on this n.g. And
certainly I jumped from set --> {group} --> metric_space with hardly a
breath and thus from <closure> to <completeness>. Why would I muck-about
without the <distance> concept ? Well of-course you may ...

Anyrate, on to that/my terrible " X + Y " notation. I was thinking ...
looks innocent enough, but can you get in trouble using the addition
operation? Pretty-dammed well ill-defined as a maths question, but OTOH
mucking-about you can find that trouble fast for the rationals:

Consider the recursion: Y(n+1) = Y(n)/2 + 1/Y(n)

I'm adding two rationals. Punch out the first-couple loops on a
calculator (Y(0)=1) and you get as close to <ROOT>_2 as you wish.
Sometimes limits run on-&-on, but sometimes they happen fast.
OOps ...
<distance> isn't a rational so poof there goes the metric space if you
want to stay "inside" the set of rationals.

True, that bit of maths won't win many awards - I won't bet $$.05 on my
terminology. Hack away if you feel the need. Let's remember what was/is
the original issue. Can one always expect a trouble-free translation from
verbal expression of a concept to some maths formulation ? I think a
"reasonable mans" answer is ... NO.

nss
*****







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