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


Re: Which naturals better?
Posted:
Feb 5, 2013 11:57 PM


In article <d7da00fc38c64089bfafa5af4ff1573a@i15g2000vbv.googlegroups.com>, JT <jonas.thornvall@gmail.com> wrote:
> On 6 Feb, 01:30, Virgil <vir...@ligriv.com> wrote: > > In article > > <229621667f374a00a88d829d8c14e...@g8g2000vbf.googlegroups.com>, > > > > > > > > > > > > > > > > > > > > JT <jonas.thornv...@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. > >  > > But it still doesn't have any magnitude, in my set your each member 1 > have a magnitude. Well i see now the brackets distinguish between sets > and list, and i guess the list is ordered while the set is not. So i > should have used the other type of brackets, but it really doesn't > matter, because you see natural numbers as positions upon a > numberline, while their really are sets formed of entities > {1,1,1} {1,1,1,1} {1,1,1,1,1}where each 1 have a start and endpoint a > magnitude.
In my world the sets denoted by {1} and {1,1} and {1,1,1}, and so on, are all the same set, the unique set having 1 as a member and having no other members besides 1.
Similarly {1,2,3} and {2,3,1} and {3,1,2} and {1, 3,2} and {2,1,3} and {3,2,1}
Are all the same set.
In standard set theory, a set is determined by which objects are members and which are not, but the order in which a sets members appear in a list of its members is irrelevant to membership.
< And zero does not qualify into these sets of naturals > because it have no magnitude, and again for you the naturals are > dotlike for me the they have enclosing fractions, basicly my set > {1,1,1} is a cut or a sum of cuts anywhere upon your numberline > example 2> 5 or 3 > 6 and so on. I do not beleive in the numberline > it is just counted entities, but the basic distinction is that the 1's > forming my set do have magnitudes since they are cuts. Now try cut out > zero upon your numberline it has no magnitude, and that is why it do > not qualify as a set forming a natural or even as a number.
MY number lines stretch from oo to +oo and all have a 0 between the positive numbres and the negative ones. And my set theories all allow the empty set, {}, having zero members.
> It is your empty buckets and they have no place in arethmetics.
But empty sets have a place in all standard set theories, and zeroes have a place in all standard arithmetics.
In fact, in base ten, you can't get past nine without having a zero. 

