Date: Feb 5, 2013 7:30 PM Author: Virgil Subject: Re: Which naturals better? In article

<22962166-7f37-4a00-a88d-829d8c14e730@g8g2000vbf.googlegroups.com>,

JT <jonas.thornvall@gmail.com> wrote:

> On 5 Feb, 09:04, Virgil <vir...@ligriv.com> wrote:

> > In article

> > <35d3dbda-612a-4ce8-ba5d-935295170...@h11g2000vbf.googlegroups.com>,

> >

> >

> >

> >

> >

> >

> >

> >

> >

> > JT <jonas.thornv...@gmail.com> wrote:

> > > On 4 Feb, 11:02, Frederick Williams <freddywilli...@btinternet.com>

> > > wrote:

> > > > JT wrote:

> >

> > > > > Building new natural numbers without zero using NyaN, in any base,

> > > > > [...]

> >

> > > > You seem to confuse numbers and digits. Both of these are true:

> > > > There is a number zero.

> > > > Numbers can be symbolized without the digit zero.

> >

> > > > --

> > > > When a true genius appears in the world, you may know him by

> > > > this sign, that the dunces are all in confederacy against him.

> > > > Jonathan Swift: Thoughts on Various Subjects, Moral and Diverting

> >

> > > No there is no zero in my list of naturals, in my list is each natural

> > > number a discrete ***items***, ***entity*** with a magnitude.

> >

> > Zero is a perfectly good "magnitude", and in ever more set theories,

> > zero is a perfectly good natural number.

> >

> > So how can you have an arithmetic of natural numbers which does not

> > allow a numeral representing the first of them??

> > --

>

> You do not listen to what i say each natural (not zero) is an entity

> with a range if they had no range you could not divide and make

> fractions not partition.

To me each natural, including zero is a number of objects that can be

in a (finite) set.

In my world a set can be empty, so that in my world zero is a natural

number.

> You can not partition zero it do not have a

> range of a natural you can not count zero into the set. Natural

> numbers is just sets of arranging an amount of single naturals, they

> all have the same magnitude when you say 7 it is an identity for set

> (1,1,1,1,1,1,1) now you can say that is (7) but the seven have

> members. Each natural identity like 7 is a set of single=1 naturals

> with magnitude and zero do not belong to that set.

>

> If you empty the set of (7) by picking out a single item there is no

> object zero. And when you count in a single natural first natural

> entity is 1 second 2.

>

> There is a language gap here for me a natural is a single 1 and 7

> seven is a set of seven members with single ones. So what would like

> me to call the one that make up your naturals. I guess in math 7 is a

> natural, to me it is an identity used for (1,1,1,1,1,1,1) this set is

> countable. The set of (7) is based on the assumption of

> (1,1,1,1,1,1,1) i am not sure what mathematicians mean by an identity,

> but it seem to me like 7 incorporates the hidden assumption of

> 1+1+1+1+1+1+1 and thus all natural numbers except for 1 is identities.

In my world (1,1,1,1,1,1,1) is a list, but not a set.

In my world a list with the same thing appearing in it more than once,

like your (1,1,1,1,1,1,1) cannot ever be a set. And the set of elements

appearing in such a list is {1}.

In my world the sets {1,2} and {2,1} are the same but the lists (1,2)

and (2,1) are different.

--