# Definition talk:Dominate (Set Theory)

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What if the injective mapping is weakened to a left-total, one-to-many relation to avoid the axiom of choice? –Abcxyz (talk | contribs) 13:05, 25 March 2012 (EDT)

Got a source? Or is this original research? --prime mover 13:17, 25 March 2012 (EDT)
I'm not really proposing anything, and I don't have a source. I just have a question. Lord Farin had some comments like in here and here. Now that I've thought about it, I'm wondering how an injection from the additive quotient group $\R / \Q$ to $\R$ can be constructed without the axiom of choice. Comments? –Abcxyz (talk | contribs) 13:31, 25 March 2012 (EDT)
Definition:Inclusion Mapping? What am I missing here? --prime mover 15:27, 25 March 2012 (EDT)
Sorry, ignore me, I misunderstood, I read $\R / \Q$ as $\R \setminus \Q$. It's late, I'm full of chicken and sleepy. --prime mover 15:28, 25 March 2012 (EDT)

I'm sure I've read somewhere that stuff like this needs AC; there is of course the $\ni$ relation (when regarding elements of $\R/\Q$ as the actual equivalence classes) which is certainly left-total and many-to-one (as we are dealing with a partition by equivalence classes here). So that avoids AC of course, but it is of limited use IMO. --Lord_Farin 03:10, 27 March 2012 (EDT)