Virgil
Posts:
7,005
Registered:
1/6/11
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Re: Which naturals better?
Posted:
Feb 5, 2013 7:30 PM
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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.
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