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. 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.