On 23 Jan., 13:57, Aatu Koskensilta <aatu.koskensi...@uta.fi> wrote: > WM <mueck...@rz.fh-augsburg.de> writes: > > On 23 Jan., 13:46, Aatu Koskensilta <aatu.koskensi...@uta.fi> wrote: > > >> To say the union of all FISs is finite is to say there is a natural > >> m such that n < m for all naturals n. > > > No. > > What does it mean to say the union of all FISs is finite, then?
It is not larger than any FIS. There is no fixed number as cardinality. We simply use oo.
Have you constructed in your head the Binary Tree that only contains all finite paths? Have you recognized the difference to the Binary Tree that also contains the infinite paths? Have you obtained what nodes make up the difference?
(Remember, Cantor's argument works by node/digits only!)