In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> 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.
On the contrary, the union of all such FISs is larger than EVERY FIS, since it cleary contains each FIS as a proper subset.
> There is no fixed number as > cardinality. We simply use oo.
Which is a fixed cardinality, and as such is often considered to be number. > > Have you constructed in your head the Binary Tree that only contains > all finite paths?
NO complete binary tree contains ALL finite paths as a COMPLETE binary tree is by definition restricted to paths of a single length: Length Paths Nodes ------ ----- ----- 1 1 1 2 2 3 3 4 7 4 8 15 . . . . . . . . . n 2^(n-1) 2^n-1
> Have you recognized the difference to the Binary > Tree that also contains the infinite paths?
There is only one (up to isormorphism) Complete Infinite Binary Tree. --