Talk:Union of Initial Segments is Initial Segment or All of Woset

Does $b$ need to be distinct from $y$? I'm not sure it does. The argument works well enough even when $b = y$. It makes the argument simpler because you only have to worry about one ordering, $\preccurlyeq$, and not have to worry about its strict counterpart. --prime mover (talk) 11:48, 8 June 2018 (EDT)


 * I thought it needed to be, but reading the proof again I think it does not. --GFauxPas (talk) 11:50, 8 June 2018 (EDT)


 * ... and I'm still trying to work out why the non-existence of a $y$ such that $b \preccurlyeq y$ implies that $J \subseteq S_{x_0}$. I expect it's obvious, but I can't see it. --prime mover (talk) 12:42, 8 June 2018 (EDT)


 * take $x_0 = y$, I changed the variable name to make it clearer. --GFauxPas (talk) 12:52, 8 June 2018 (EDT)


 * But you've just disproved the existence of such a $y$. How does it work that $J$ is a subset of an initial segment of a non-existent object? Sorry, but I must be missing something here, I can't get my head round it. --prime mover (talk) 04:54, 9 June 2018 (EDT)