Re: abundance of irrationals!)
- From: Virgil <ITSnetNOTcom#virgil@xxxxxxxxxxx>
- Date: Wed, 04 May 2005 15:42:45 -0600
In article <MPG.1ce3022d6275946f989bbc@xxxxxxxxxxxxxxxxxxxxxxxxx>,
Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:
> Virgil said:
> > In article <MPG.1ce2ea00faae46a4989bb5@xxxxxxxxxxxxxxxxxxxxxxxxx>,
> > Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:
> >
> > > Richard Tobin said:
> > > > In article <MPG.1ce2cce53ffd483e989baf@xxxxxxxxxxxxxxxxxxxxxxxxx>,
> > > > Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:
> > > >
> > > > >Well, then, when we get arbitrarily close to infinity in limits, have
> > > > >we
> > > > >achieved infinity? If not, what makes it different?
> > > >
> > > > A limit of infinity doesn't involve any "getting arbitrarily close to".
> > > > It just means getting (and remaining) bigger than any finite value.
> > > >
> > > > -- Richard
> > > >
> > > Bigger than finite=not finite=infinite. So it means becoming and staying
> > > infinite, but not close to any infinite value? Sure. A verrry important
> > > point.
> > > Thanks for clarifying that.
> >
> > You are missing a delicate point.
> >
> > Saying that something gets bigger than any finite number at some point
> > does not say that it gets bigger than all finite numbers at any point.
> >
> > This involves the same reversal of quantifiers that WM can't, or won't
> > comprehend.
> >
> > Getting bigger, at some point, than any particular number:
> > For each n in N there is an m in N such that m > n.
> > (true since ther exists m = n+ 1 < n for every n)
> >
> > Getting bigger, at some point, than every number:
> > There is an m in N such that for every n in N, m > n.
> > (false since we never have m > m)
> >
> When you say "It just means getting (and remaining) bigger than any finite
> value.", are you referring to some particular finite value, or each and every
> finite value. When you use a word like "any" in this context, the natural
> reading of it is "any one that exists", which sounds like a set of all finite
> numbers.
"Any" means one at a time, while all means "simultaneously" or "all at
once".
It is quite feasable that a good fighter "can beat any man in the house"
one at a time without being able to beat all of them at once.
> If you are saying that a limit as x goes to oo means x is bigger
> than
> SOME finite number, sorry, you're wrong.
To say that "x goes to infinity" means for every finite y, there is a
value that x can take which is larger than that y.
For all (finite) y, there is an x such that x > y.
> This really has nothing to do with
> the
> logical constructo issue you mention, which makes me imagine WM doesn't
> really
> have a problem with it, but it's just part of your toolbox of argument
> maneuvers to confuse your "opponents".
If you do not know enough about the mathematics of natural numbers to
understand what any serious math student understands, how is that my
fault?
.
- References:
- Re: abundance of irrationals!)
- From: Randy Poe
- Re: abundance of irrationals!)
- From: aeo6
- Re: abundance of irrationals!)
- From: Richard Tobin
- Re: abundance of irrationals!)
- From: aeo6
- Re: abundance of irrationals!)
- From: Virgil
- Re: abundance of irrationals!)
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