Talk:König's Tree Lemma

The following statement is superfluous and should be removed. --Ilan 05:03, 23 April 2012 (EDT)


 * Each $t_n$ has infinitely many descendants.


 * I disagree. You need to suppose that $t_n$ has infinitely many descendants in order for the induction to work.
 * If there is a different proof which does not require this hypothesis, then that is a different proof and needs to be entered as such.
 * On the other hand, if you can see this proof working without that hypothesis, feel free to amend it accordingly. --prime mover 08:15, 23 April 2012 (EDT)
 * My point is that the first two conditions are necessary as a statement of the result, while the third is only used in the proof. I can modify the proof in order to clarify this distinction. --Ilan 16:50, 23 April 2012 (EDT)
 * Which would make it a separate proof, yeah? As it stands, the "infinite descendants" is part of the proof, not part of the statement of the result. --prime mover 17:03, 23 April 2012 (EDT)

Induction
Prime.mover, it is NOT a proof by induction. At each step, it makes an arbitrary choice. The minimal correction is to use the Axiom of Dependent Choice.

The minimal choice principle that can be used to prove the theorem is almost certainly the Axiom of Countable Choice for Finite Sets. --Dfeuer (talk) 22:15, 26 May 2013 (UTC)


 * Since when are we not allowed to fix mathematical errors? --Dfeuer (talk) 23:06, 26 May 2013 (UTC)