# On the tags (transfinite-induction) and (transfinite-recursion)

At the moment we have two tags and . These topics are rather close.

I can imagine a reasonable question which could be tagged with the tags , , , . Having only five spots for tags, this might become a problem at some point (at least for some questions.)

Transfinite induction and transfinite recursion are not the same, but these two topics are definitely close to each other. Basically the difference is that in one case we are proving some result by induction on ordinal numbers. In the other case we are proving existence of some object using this technique. (I have decided to be cautious and avoided using work "constructing" or "defining" some object, but for informal description they might sound better and make the distinction clearer.)

• Would it be better to have these two topics in the same tag? If we want to create one tag for both topics, what would be the name of the new tag? Or should we simply create synonym between the two tags in one direction?
• Should we use simply to tag questions about transfinite induction/recursion? If yes, then should there be a synonym from these two tags to the master tag (ordinals), or is it sufficient to remove the tags and explicitly mention in the tag-info for ordinals that the tag is intended also for these question?
• Or is the situation satisfactory as it is currently and it is better to keep two separate tags to make the distinction?

The tag was created in August 2015 and it has 46 questions.

The tag is older, first occurrences can be found in June 2011. The tag contains 65 questions.

• I would probably consider a synonym (transfinite-recursion) $\to$ (transfinite-induction) as a reasonable way to go. I think the topics are close enough to each other, yet still important to warrant a separate tag. But I'll wait a bit to see what other people think. (And later I might possibly post an answer with this suggestion, unless somebody does that before me or some arguments in this discussion show me that this is not a good idea.) – Martin Sleziak Apr 15 '18 at 8:09
• I should probably also mention that I have pinged the creators of both tags to let them know about this discussion. – Martin Sleziak Apr 15 '18 at 8:10
• Induction and recursion are different things, even if there are some (formal) similarities. Mixing them up tagwise will only help confuse those that are not clear on the distiction. – Andrés E. Caicedo Apr 15 '18 at 12:41
• @AndrésE.Caicedo Why not expanding your comment a bit and posing it as an answer? The way I understand your comment, you're for preserving the current status, i.e., leaving the tags separate. – Martin Sleziak Apr 15 '18 at 14:21