Date: Mar 18, 2013 3:02 AM
Author: fom
Subject: Re: Matheology § 224
On 3/18/2013 1:39 AM, Ross A. Finlayson wrote:

>

> So, the question is, if Virgil says there exists

First, although I have not read that signature

element too carefully, I doubt Virgil is claiming

that anything exists. WM made a claim. Virgil

is demanding proof of the claim according to the

standard meaning of the terms.

> a field over [0,1],

> or the elements of the CIBT or Cantor set, there would be a continuous

> function f: R_[0,1] <-> R that had a (+) b = f^-1(f(a)+f(b)) and a (*)

> b = f^-1(f(a)f(b)), and that f(ab) = f(a)f(b) and f(a) + f(b) = f(a

> +b).

You are making a mistake in these equations.

The multiplication in the definition,

f(x+y) = f(x) + f(y)

f(ax) = a*f(x)

is a scalar multiplication.

Of course, so much mathematics is done in

familiar number systems where the scalar

domain is related to the arithmetic of the

additive abelian group that one does not

think twice about it.

This is different. There is no definition

for multiplication of sequences from the

binary tree as sequences in the binary tree.

Linear mappings in this sense are not

immediately about continuity. Continuity

is a topological property. Linearity in

this sense is an algebraic property.

>

> So from an apocryphal comment that there is a linear mapping and thus

> vector space and field over [0,1], I wonder how Virgil backs this

> claim, as I well imagine it's not a linear function with f(0) = -oo

> and f(1) = oo. (And it is.)

>

Virgil is not making a claim. He is asking

that a claim be substantiated.

> Then, about compact admissibility

<snip>

It is a pretend construction that was

done to give you an idea of what might

be required for WM to meet Virgil's

expectations.

I would be required to do some work

to make it something you could put

on a wikipedia page....