Date: Mar 24, 2013 11:28 PM
Author: ross.finlayson@gmail.com
Subject: Re: Matheology § 224
On Mar 24, 7:37 pm, Virgil <vir...@ligriv.com> wrote:

> In article

> <a2ef4e0f-a37a-4795-886f-7fb3786cc...@vh9g2000pbb.googlegroups.com>,

> "Ross A. Finlayson" <ross.finlay...@gmail.com> wrote:

>

> > Are you saying that lim_n->oo Sum_i=1^n 1/2^i =/= 1, or, that

> > Sum_i=1^oo 1/2^i = 1?

>

> I was not saying either.

>

>

>

> > Then, where the lines are n-sets: what is the union of the lines?

>

> What do you mean by "n-sets"? Do you mean what WM calls FISONs.

>

>

>

> > The sum of all the finite numbers (natural integers): isn't a finite

> > number, and for no finite number is it their sum. Yet, addition is a

> > closed operation in the integers. That gets into the difference

> > between operations that are closed for finitely many, and unboundedly

> > many, and infinitely many applications of the operation, here

> > addition. The transfer principle

>

> Which does not exist, so let us ignore it, and all following garbage..

> --

No, if you'll excuse it, an n-set is any set with n-many elements

(natural integers). Used in combinatorics, various results of n-sets

are simply coded {1, 2, ..., n} in combinatorial enumeration, so,

initial n-sets, say.

The transfer principle most certainly does exist, for example a set

(operation of union) of sets is a set, a sum of integer sums is a sum,

and etcetera.

No, there's general interest in the features of mathematical objects,

moreso in the less obvious, less overstated, and less obnoxious.

Regards,

Ross Finlayson