Virgil
Posts:
8,833
Registered:
1/6/11


Re: Which naturals better?
Posted:
Feb 5, 2013 7:30 PM


In article <229621667f374a00a88d829d8c14e730@g8g2000vbf.googlegroups.com>, JT <jonas.thornvall@gmail.com> wrote:
> On 5 Feb, 09:04, Virgil <vir...@ligriv.com> wrote: > > In article > > <35d3dbda612a4ce8ba5d935295170...@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. 

