On Friday 16 July 2004 18:23, Jonadab the Unsightly One wrote:
> > Please take my words as my understanding, ie. with no connection to
> > mathmatics or number theory or whatever. I'll just say what I
> > believe is practical.
>
> [...]
>
> > I'd believe that infinity can be integer, ie. has no numbers after
> > the comma; and infinity is in the natural numbers (?), which are a
> > subset of integers.
>
> If that were the case, 0/Inf would == 0.
Isn't that so?
0/+Inf == 0
0/-Inf == 0 (or -0, if you wish :-)
> Also, if that were the case, 0..Inf would be a finite list. (It is
> trivial to prove that 0..N is a finite list with finite cardinality
> for all natural numbers N. So if you set N equal to Inf, 0..Inf would
> have finite cardinality, if Inf is a natural number.)
>
> This is obviously some new definition of Inf of which I was not
> previously aware.
Well, after reading my sentence one more, I see what may have caused some
troubles.
Inf is not in N; but *in my understanding* it fits naturally as an extension
to N, that is, Inf is (or can be) integer as is "after" N...
This won't be written in math books, I know.
> Also, if that were the case, 0..Inf would be a finite list. (It is
> trivial to prove that 0..N is a finite list with finite cardinality
> for all natural numbers N. So if you set N equal to Inf, 0..Inf would
> have finite cardinality, if Inf is a natural number.)
If I extend the natural numbers N with Inf to a new set NI (N with Inf), then
0 .. n (for n in NI) need not be finite ...
Sorry for my (very possibly wrong) opinion ...
Regards,
Phil
