# Definition talk:Generator

Definition of Finitely Generated is wrong in my opinion: I think it's better give a link to order of a set. joel talk 00:18, 10 January 2013 (UTC)

Good call. Refactored it while I was about it, that one had got missed. --prime mover (talk) 06:23, 10 January 2013 (UTC)

## Disambiguating

I'd rather put these on separate pages. Lots more definitions of generators to come. --barto (talk) (contribs) 14:37, 8 November 2017 (EST)

Take a look at Definition:Generated --barto (talk) (contribs) 15:08, 8 November 2017 (EST)
Done; and added red links to unrelated notions. --barto (talk) (contribs) 16:41, 15 January 2018 (EST)

## Generated vs. generator

Regardless, "generated sub[structure]" is a more primitive notion: it defines something, rather than giving a name to something whose existence is assumed. Thus the cleanest way seems to be to make "Generator of X" a subpage of "Generated Sub-X". --barto (talk) (contribs) 14:50, 8 November 2017 (EST)

Actually, having put the idea to rest for a while, I think it's better to define generator and generated at the same time, as it was and still is on some pages. Thoughts:
1. The subtlety I mentioned at Definition talk:Generator of Module will remain, whatever the way in which the definitions are structured: the substructure generated by a subset of a substructure is the same as when considered as a subset of the whole structure.
2. One of the two notions may be argued to be more primitive than the other, but such distinction is largely artificial.
3. The two are always defined in the same breath.
4. The different definitions for generator and generated really are the same, as are their equivalence proofs.
That is; I propose to merge all generator of X into generated sub-X. --barto (talk) (contribs) 16:57, 15 January 2018 (EST)