Virgil
Posts:
4,482
Registered:
1/6/11
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Re: ZFC and God
Posted:
Jan 23, 2013 3:01 PM
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In article
<8f5eaf36-060c-462d-bcc5-f9d57b2fe241@l13g2000yqe.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> 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.
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