Re: infinity
- From: Virgil <ITSnetNOTcom#virgil@xxxxxxxxxxx>
- Date: Thu, 13 Oct 2005 16:48:25 -0600
In article <MPG.1db867926204e8c098a489@xxxxxxxxxxxxxxxxxxxxxxxxx>,
Tony Orlow <aeo6@xxxxxxxxxxx> wrote:
> stephen@xxxxxxxxxx said:
> > What does that mean? You are equating "being larger than any
> > finite value you can choose" with "for any finite value you choose,
> > you can find a larger finite value."
> >
> > If you meant something else, what did you mean?
> I read those as being equivalent, and not meaning "larger than EVERY
> finite number".
Then TO is being stupid again, as that is precisely what it does mean.
Does TO imply that there is a "finite number that you cannot choose"
which is larger?
> you trying to make it look like I said "if for all x there exists y
> s.t y>x then there exists y s.t for all x y>x. I never said that.
If y is "larger than any finite value you can choose" then for any (and
every) x, y > x.
> >
> > > I said the opposite, that just because you can find a finite
> > > greater than any given finite, that greater finite is still
> > > finite. If one claims that the set size is greater than any
> > > finite you specify, that does NOT mean it's infinite, since there
> > > is always a FINITE number greater than any finite you specify.
TO is saying
if (for all x there is a y with y > x) then (there is a y with for
each x, y > x).
TO's quantifier dyslexia is kicking in again!
> >
> > You are making the same mistake. If I claim that X is larger than
> > any finite Y you can specify, then there does not exist a finite
> > larger than X. This is the exact opposite of the claim that I can
> > find a finite Y larger than X.
> No, you are equating "x is larger than any finite I specify" with "x
> is larger than ALL finite values."
Wrong! If x is larger that any finite that CAN BE specified then no
finite exists larger than x.
> When you state the first, I say
> that doesn't mean x is infinite, because there is always a larger
> finite value than any finite value you specify. It doesn't prove that
> value is infinite, just that it's bigger than any finite you specify.
if it is a natural bigger that any finite that CAN BE SPECIFIED, then
either there are unspecifiable finites ( impossible in the naturals) or
it is not finite.
TO seems unable to grasp that not finite means infinite.
> >
> > If one claims that the set size is greater than any finite you
> > specify, then it does mean its infinite. You name a finite number,
> > and the set size is larger than that. The set size does not change
> > from guess to guess. That cannot be true if the set size is a
> > finite number.
> Escept that, for any finite number you specify, there is always a
> FINITE number greater than it. This is why the largest finite can
> never be especified. It's larger than any finite you do specify.
I specify "the largest finite plus 1", if it exists then if is not the
largest, and if it doesn't exist there is no problem.
> It's still finite.
In TO's dreams is the only place it exists at all.
> >
> > > I don't need you mal- paraphrasing what I've said, thank you. You
> > > are obviously not an authority on what I've said, since you are
> > > obviously not paying very close attention to what it is I say.
> > > So, I'll thank you to stop trying to make my position look
> > > stupid. It reflects more on you than on me.
> >
> > I am paying attention to the words you actually use. You
> > apparently to do not know what the words you use mean.
> I do but you don't seem to.
We mean TO does not seem to know what they mean outside of his TOmatic
twilight zone. What they mean inside it is irrelevant to mathematics.
> >
> > If X is greater than any finite number, than X cannot be finite.
> > You claim this is false, but your argument only makes sense if you
> > change the orders of the quantifiers.
> No, if you say "x is greater than EVERY finite number", THEN it's
> infinite.
When we say greater than every finite, we mean greater than every
finite. And every bound on the set of finite naturals must be greater
than every finite, since it vcannot be any one of them that has a
successor.
If TO maintains that there is finite upper bound on the finite naturals,
let him name it. His usual and-waving fails.
> >
> > When we say that X is greater than any finite number Y, we mean
> > that for any finite number Y you specify, X>Y. We do not change
> > what X is everytime you pick a new Y. X is chosen first, and it
> > does not change, and it is greater than every Y.
>
> Let's look at Randy's original statement:
> > > We would like to characterize the size of the set of finite
> > > naturals. It is pretty clear that no finite value can serve as
> > > that size, that whatever the size is, it's bigger than any finite
> > > value you choose.
> This is equivalent to saying, for any specific finite x, the set size
> y is larger than x. If the statement were that the set size is larger
> than EVERY finite value, then it would be equivalent to saying it's
> infinite.
Then TO must be able to name some finite that it is NOT larger than, or
they actually are equivalent.
TO repeated arguments that what are equivalent staements are not
equivalent statements have been snipped.
.
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- Re: infinity
- From: Jonathan Hoyle
- Re: infinity
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