[Info-vax] VMS process communication

[Dan Cross]

In article <330ad98a-f752-49f4-b1c0-5cd674487fa5n at googlegroups.com>,
Steven Schweda  <sms.antinode at gmail.com> wrote:
>> Otherwise we're talking about infinite series of sums. [...]
>
>   The usual definitions are:
>
>      Sequence: a set of numbers.

Errm, hmm.  This is insufficient.  Order matters in a sequence,
and the elements of a sequence are enumerable.  Plus, elements
can be repeated.  One can define an isomorphism between a
sequence and, say, a subset of the naturals that would represent
each element as a tuple, with f: S -> N x S where F(s) = (s, k)
for k the index of s in the sequence, and with f': N x S -> S
being projection.

>      Series: the sum of the terms in a sequence.
>
>
>> [...] you will never compute the final value of an infinite series...
>
>   Watch me.  S = 1/2 + 1/4 + 1/8 + 1/16 + ... = 1
>
>   2 * S = 1 + S.  Work it out.

The basic idea here is correct; summing an infinite sequence has
some value if the series is convergent.  The value of that
geometric series really is exactly 1, in the same way that
0.11111111... really is exactly 1/9.

Regardless, Johnny's original definiton of Pi was correct.

	- Dan C.