Re: abundance of irrationals!)
- From: imaginatorium@xxxxxxxxxxxxx
- Date: 1 May 2005 10:46:14 -0700
mueck...@xxxxxxxxxxxxxxxxx wrote:
> imaginator...@xxxxxxxxxxxxx wrote:
> > aeo6 Tony Orlow wrote:
>
> > > The fact is that one cannot have an infinite set of finite
numbers,
> > if the difference
> > > between any two is at least 1, whiich is true of natural numbers.
> >
> > That's a _fact_, is it? I mean, not just something you worked out
for
> > yourself?
> >
> > Anyway, given this 'fact', suppose I've tried to make an infinite
set
> > of finite numbers at least 1 apart - to keep it absolutely safe,
I'll
> > make the set of even integers {0, 2, -2, 4, -4, ... }. Now I think
> > there are an infinite number of even integers,
>
> Do you really? Where starts infinity?
Huh? "Infinity" doesn't "start" anywhere...
> because I don't think
> > that if I start counting them, that I will ever stop.
>
> That s potential infinity.
Yes, that's a slightly old-fashioned terminology (because actually the
"actual/potential" distinction isn't very coherent). But that's all set
theory means by describing a set as 'infinite': you can't count the
elements by reciting a ditty (eins, zwei, drei... : whatever) and hope
to stop.
> But that is not mant by set heory, because
> it does not supply a cardinality, in particular it does not lead to
> aleph_0.
Rubbish. Like most cranks, you have not the faintest clue what the
theory you claim to be disproving actually says.
> Does your 'fact'
> > mean that actually some of these even integers are actually
infinite?
> > Suppose it must, no?
>
> As long as the number of your numbers counted is finite, the
magnitudes
> will be finite. If one of them changes, the other will change too
> simultaneously.
Sounds exotic. You mean that one of my even (finite, normal) integers
(call it P) is perfectly OK one minute, then it suddenly changes? Into
a different number? Sounds more like Fortran programming than maths...
*
-----------------------
*I'm thinking not so much of P=P+1 as
SUBROUTINE CHANGE(X, Y)
X=Y
RETURN
END
Now try:
CALL CHANGE(2, 3)
-----------------------
> > OK, how many of them are infinite?
>
> Precisely as many as do not fit into a finite set.
"Do not fit"? Tell me, pray, how many do "fit into a finite set"? Is
this some particular number, or can I expect some numbers to fit one
minute, then jump out the next?
Anyway, this is obviously a waste of time.
Brian Chandler
http://imaginatorium.org
.
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