Date: Mar 22, 2013 3:42 PM
Author: fom
Subject: Re: Matheology § 224
On 3/22/2013 5:14 AM, WM wrote:

> On 22 Mrz., 10:49, fom <fomJ...@nyms.net> wrote:

>> On 3/22/2013 4:13 AM, WM wrote:

>>

>>> On 22 Mrz., 09:54, Virgil <vir...@ligriv.com> wrote:

>>>> On 3/22/2013 1:38 AM, WM wrote:

>>

>>>>> This proves that we can remove all finite lines from the

>>>>> list without changing the contents of the remaining list. And this is

>>>>> remarkable, isn't it?

>>

>>>> Since WM also claims that all the lines of that list are finite lines,

>>>> WM is now claiming one can trow out the entire contents of a list and

>>>> still have the entire original list in place.

>>

>>> That is a consequence of the completed infinity of set theory.

>>

>> He is referring to your claims

>

> I know. They are a consequence of finihed infinity.

>>

>>

>>>> Unfortunately, as in the above claim, what WM claims to be the case

>>

>>> can be proven by induction that holds for every finite line.

>>> Every number that belongs to line n belongs to the next lines too.

>>

>> It should be observed, once again, that the most WM is ever referring

>> to with statements like this is the form of the domain for an

>> induction rather than any true use of inductive proof.

>

> True use of inductive proof has been fonuded by Fermat without any

> reference to domain. Your "true use" refers to "the only method you

> have been taught".

I missed this one.

Once again, WM is turning back to a time

before axiomatic mathematics.

He just posted 228 in which it is acceptable

to have the pure imaginary unit as a number.

What then is a number? If there are different

kinds of numbers, what distinguishes numbers from

non-numbers? What do we call a collection of given

numbers that are the same type? Would that be

a number system? What is the criterion for calling

an arbitrary collection of objects a number system?

Would that be an arithmetical calculus?

Why should any arbitrary collection of objects

with an arithmetical calculus not be called a

number system?