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:
 * 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.
 * One of the two notions may be argued to be more primitive than the other, but such distinction is largely artificial.
 * The two are always defined in the same breath.
 * 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)