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