Actually, if we are to have sophistication-graded tags for set-theory, then it's a bit crazy that transfinite induction belongs in elementary set theory (explicitly according to the tag excerpt). How is one supposed to tag actually elementary set stuff, I wonder?
@Eugene i don't see anything wrong with it as a question. i can't say i fully understand it, but if there's an error made in your question, it seems like it would be instructive for an answer to point this out, and i cannot see how down-voting is called for.
@DavidWheeler oh seriously the downvoting isn't an issue. recently i've been frequently downvoted without explanation. i'm sure there's a troll somewhere.
@Eugene But I don't think there is much relevant overlap between ordinary induction in $\mathbb N$ and the transfinite stuff. Formally one is a special case of the other, of course, but the questions one could ask about either are very different.
