Virgil
Posts:
4,499
Registered:
1/6/11
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Re: Which naturals better?
Posted:
Feb 5, 2013 7:14 PM
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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.
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