Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: Which naturals better?
Replies: 41   Last Post: Feb 8, 2013 3:49 AM

 Messages: [ Previous | Next ]
 JT Posts: 1,448 Registered: 4/7/12
Re: Which naturals better?
Posted: Feb 5, 2013 11:35 PM

On 6 Feb, 01:30, Virgil <vir...@ligriv.com> wrote:
> In article
>
>
>
>
>
>
>
>
>
>  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.
>
>
>
>
>
>
>
>
>

> > 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. 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.
It is your empty buckets and they have no place in arethmetics.

Date Subject Author
2/4/13 JT
2/4/13 Virgil
2/5/13 JT
2/4/13 Frederick Williams
2/4/13 JT
2/5/13 JT
2/5/13 JT
2/5/13 JT
2/5/13 JT
2/5/13 JT
2/5/13
2/5/13 JT
2/5/13 Virgil
2/5/13 JT
2/5/13 Virgil
2/5/13 JT
2/6/13 Virgil
2/6/13 JT
2/6/13 Virgil
2/6/13 JT
2/6/13 Virgil
2/6/13 JT
2/7/13 Virgil
2/5/13 Virgil
2/5/13
2/5/13 JT
2/5/13 Virgil
2/5/13 JT
2/5/13 JT
2/6/13 Virgil
2/6/13 JT
2/6/13 Virgil
2/6/13 JT
2/6/13 Virgil
2/7/13 Brian Q. Hutchings
2/5/13 Virgil
2/5/13
2/5/13 Frederick Williams
2/5/13 Virgil
2/7/13 HOPEINCHRIST
2/7/13 Brian Q. Hutchings
2/8/13 JT