As before, we need the lemma that the union of any finite set of finite collections is finite. The trick is to first construct a function f on the nodes such that if x has an infinite subtree then f(x) is a child node with an infinite subtree. This is possible because of the lemma. Now we can then build the path using f and the recursion theorem.

This is possible because for any path that ends at a node x with an infinite subtree, f(x) is a child node with an infinite subtree and so we can extend the path to f(x). Since f is a function, we are not making any choice here.

So the only use of CCF is to construct f.

Oh wait there's something wrong.

← 4 messages moved from Logic

@RichardU Not true, that stuff is done all the time ;) I did it yesterday to provide more context on a comment I left Em... Stuff that would have been too chatty on main

You know, trashtalking someone else right in front of them is decidedly not nice

@D.Hutchinson Like I already said this morning, we constantly have to tolerate you too... so please don't sidetrack the discussion and stop calling people out.

You should really handle that in private

This way you only attract more derision

@Tinkeringbell I think a bit more restraint is in order.

THIS ^^^^^^^^^^^^

Alternatively, custom moderator flag on any post

I concur

Oh.. okay!

We'll drop it ;)

Remember, any time I start sounding reasonable should be a red flag to everyone.

:D

← 14 messages moved from The Awkward Silence