Talk:Injection Image of Set Difference
Jump to navigation
Jump to search
In fact, the converse holds (a function preserving set difference is injective). How would I proceed adding this result to the present page? --Lord_Farin 16:41, 12 March 2012 (EDT)
- I'd start with One-to-Many Image of Set Difference and prove it for the general relation.
- Actually I'm surprised, I thought I'd already done this proof both ways round, must have forgotten.
- Take Image of Intersection under One-to-Many Relation as a model, and the corresponding proof for injections, I'd guess. --prime mover 17:11, 12 March 2012 (EDT)
- I must have been unclear; I have a proof here in my reference work (and otherwise, I would deem myself capable of producing one). The problem I raise is that it is apparently undesirable to change theorem statements (as discussed frequently past week), and I was asking how to incorporate the stuff in the appropriate way. --Lord_Farin 17:19, 12 March 2012 (EDT)
- What about something like what's done with these? Derivative of Constant,Zero Derivative implies Constant Function.--GFauxPas 17:22, 12 March 2012 (EDT)
- Yes all right, I overreacted when I said what I said the other day about changing existing results, but then a) there was a mess last week, and b) the statement was amended but the proof was not modified to take that amendment on board.
- (Sorry about that, I mistakenly thought that the proof already up was sufficient. --GFauxPas 17:39, 12 March 2012 (EDT))
- You could be right. If it was (and is), then I apologise. --prime mover 18:42, 12 March 2012 (EDT)
- (Sorry about that, I mistakenly thought that the proof already up was sufficient. --GFauxPas 17:39, 12 March 2012 (EDT))
- Yes all right, I overreacted when I said what I said the other day about changing existing results, but then a) there was a mess last week, and b) the statement was amended but the proof was not modified to take that amendment on board.
- But generally, turning an if into an iff, there's usually no obvious problem with an existing page being expanded, so I'd say just expand it like as for the Intersections result. But again, rather than just prove the result for injections, can it be proved for one-to-many relations? Does it hold for one-to-many relations? That's what I meant when I said "take blahblah as a model", I didn't mean for how to write the proof, I meant for how to structure the page(s). --prime mover 17:29, 12 March 2012 (EDT)
Both this and One-to-Many Image of Set Difference have been expanded, is it to your liking? --Lord_Farin 06:10, 24 March 2012 (EDT)