Virgil
Posts:
6,985
Registered:
1/6/11


Re: Which naturals better?
Posted:
Feb 5, 2013 7:14 PM


In article <5110EC4D.CB8986EB@btinternet.com>, Frederick Williams <freddywilliams@btinternet.com> wrote:
> JT 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. > > > > No there is no zero in my list of naturals, in my list is each natural > > number a discrete ***items***, ***entity*** with a magnitude. > > Fairy snuff. It used to be common to define the natural numbers as > these: 1, 2, 3, ... Now 0, 1, 2, 3, ... is more common. If you prefer > the older definition I doubt that people will mind. > > Zero is quite useful even if you don't want to call it a natural > number. For example, one may have no money in one's bank account. How > many pennies (cents, etc) is that? Zero.
And zero as a natural arose. in part. as being the size of a finite set. For example the von Neumann naturals ARE naturally sets in ZF or ZFC with 0 = {} and n + 1 = n union {n} so 1 = {{}} = { 0 } 2 = { {}, {{}} } = { 0, 1 } 3 = { {}, {{}}, {{},{{}}} } = { 0, 1, 2 } and so on, and so on. 

