On Sunday, December 4, 2011 4:10:29 PM UTC-5, WM wrote:
> > But there is no reason to believe it is true for the set of ALL > > FISONs. In particular, the statement: > > > > The union of any collection of FISONs is another FISON. > > > > is false, > > That is a statement of belief.
No, it's provable.
Theorem: If X is a FISON, then there is a FISON Y such that Y is NOT a subset of X.
Proof: Every fison has a largest element. So let the largest element of X be n. Then let Y = N union { n+1 }. Then Y is not a subset of X.
Theorem: If U is the union of all FISONs, and X is any FISON, then X IS a subset of U.
