Re: OT: White Goddess

Hi!

Andreas Johansson <and_yo@...> writes:
> >But it isn't a polygon with an infinite number of sides, because the
> >length of each of those sides would have, perforce, to be zero, which
> >means that the circumference, being a sum of zeros, would be zero.
>
> According to your reasoning, if I took a line 1m long and divided it into an
> infinite amount of pieces the total length of the fragments would be zero.
> 1m has disappeared without anyone removing any length, eh?
You cannot calculate like that.  What works for finite numbers does
not work for infinity.  See why:
   a) with infinitely many pieces, you cannot add them by iterating
      (you will not stop working)
   b) with infinitely many pieces, you cannot multiply a finite
      length > 0 with infinity to get to a finite result
   c) assuming each piece has length 0, you still may not multiply
      0 times infinity.  It is like dividing by zero.

When you use infinity, you must change the rules of calculating.  And
that's what you do: you call it a curve, not a polygon.

**Henrik