Virgil
Posts:
4,663
Registered:
1/6/11
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Re: Which naturals better?
Posted:
Feb 5, 2013 11:57 PM
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In article
<d7da00fc-38c6-4089-bfaf-a5af4ff1573a@i15g2000vbv.googlegroups.com>,
JT <jonas.thornvall@gmail.com> wrote:
> On 6 Feb, 01:30, Virgil <vir...@ligriv.com> wrote:
> > In article
> > <22962166-7f37-4a00-a88d-829d8c14e...@g8g2000vbf.googlegroups.com>,
> >
> >
> >
> >
> >
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> > JT <jonas.thornv...@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.
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> > > 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.
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