piclist 2001\06\03\015012a >
Thread: Brain Burp Rounding??
face BY : David VanHorn email (remove spam text)

>Its value is exactly 1.

So I did a little digging, and found this link.

However, all that is said about a converging series is that you can
determine a value that it approaches.  I see no requirement or statement
that it REACHES that value.

Here also,

S = 1/2 + 1/4 + 1/8 + 1/16 + ... + 1/2^n + ...

This series is described as convergent (obvious) and approaching 1, but not
described as being  equal to 1


Finally the statement:
If the sequence of partial sums of an infinite series has a limit, then
that limit is the sum of the series.

Looks to me like we are defining "sum of the series" as something special,
and we are not saying that the series is equal to the limit, in a manner
similar to the way that "spin" is used in quantum mechanics.

It's certainly useful in calculation, because it causes those awkward
infinities to dissapear, by ignoring the infinitely tiny difference between
the actual result, and the defined result.

Inverting Zeno's paradox, the fallacy is that a finite distance (or number)
does not become infinite, simply because it can be divided into an infinte
number of smaller distances (or numbers)

Dave's Engineering Page: http://www.dvanhorn.org

I would have a link to FINDU here in my signature line, but due to the
inability of sysadmins at TELOCITY to differentiate a signature line from
the text of an email, I am forbidden to have it.

http://www.piclist.com hint: The PICList is archived three different
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