Re: The Paradox of Zeno

From: Virgil (ITSnetNOTcom#virgil_at_COMCAST.com)
Date: 11/12/04 

Date: Fri, 12 Nov 2004 13:13:35 -0700

In article <q9Zkd.9404$WC6.4055@bignews3.bellsouth.net>,
 "eleaticus" <eleaticus@bellsouth.net> wrote:

> "Virgil" <ITSnetNOTcom#virgil@COMCAST.com> wrote in message
> news:ITSnetNOTcom%23virgil-070B9F.22451811112004@comcast.dca.giganews.com...
>
> Stick to poetry, Virgil.

Since eleaticus cannot refute my statements, he has to snip them.

<unsnip, including eleaticus' idiocies>

> In long and short it would be nice were you not to serve idiocy so well. In
> many 'sciences' there are calculation formulas that are shorter or more
> convenient ways to calculate a result, but it is the definitional formula,
> not the calculation - or proof of theorem - formula that tell us what is
> what.

And the definitional "formula" for convergence of a sequence in standard
analysis does not mention infinity, at least in any of the math texts or
handbooks I have ever seen. the epsilon-N definition above, or more
topologically expressed variants, is pretty much what all of them use.
>
> Go back, poopynoncompos, and present us with the original, definitional
> formula for an infinite series and tell us how that formula contains no
> infinity.

A real infinite SEQUENCE is a mapping from the set of natural numbers,
N, to the set of real numbers, R.

For a given sequence, the corresponding series is the sequence of
"partial" sums as define above, i.e., given sequence
f:N -> R : n -> f(n) then the corresponding series is
g:N -> R : n -> Sum_{m <= n} f(m)

Since every series is also a sequence, convergence of series means
convergence as a sequence.
>
> It is not pure idiocy, I know, that makes you an unreasonable ***, and
> probably not pure malevolence, but the latter is a lot closer to being the
> cause than the former.

If there is any unreasonableness or malevolence here, it is generated
only by those who reject standard definitions without justification.
>
> Show us the infinite series formula that contains no infinity.

BEHOLD: the injection f: N -> R: n -> n contains no infinite number,
though it involves sets which are not of finite cardinality.
>
> I look forward to it.

<end unsnip>

If eelyaticus looked forward to it so much, why did he snip all of it?
>
> Zeno's basic (continuous space and time) paradox can be defined algebraicly
> as distance travelled D = sum(D/2^n), n=>infinity and no amount of schizoid
> math will change the fact that the PROCESS involved is sequential, and the
> end of the sequence will never occur, being an infinite sequence. Not
> algebraicly sequential, but physical sequential, meaning only one step can
> be taken at a time.
>
> No formula that tells us WHAT the sum would be IF the last step could be
> taken can make even step infinity-1 occur.

There is no such thing as a "last before reaching infinity" step.

Unless eeleaticus can show that time is quantized so that there is an
indivisible small time quantum, there is no difficulty in taking
infinitely many shorter but briefer steps in a finite but infinitely
divisible time interval.

If one moves one metre in one second and half a metre in the next half
second and a quarter metre in the next quarter second, an keeps moving
at that same constant velocity on one metre per second, does eeleaticus
foresee any problem in eventually covering a full two metres?
>
> Hell, the formula tells us what the sum would be IFF.
>
> If any formula could make the sequence conclusable, it could tell us how
> great the last step is. The size of the last step/distance would necessarily
> be definable.

"Last step"? If Eleaticus were before correctthat there was no "last
step", why is he now arguing that there ought to be one?
>
> Yes, why don't you tell us what that distance is? Let D=100. Simple matter
> to tell us the last subdistance in a distance covered, what?

That "last", being non-existent as a distance, must be zero as a
distance.

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