Talk:Domain of Small Relation is Small

$A$ is not required to be small. It is only required to be a mapping. Image of Small Class under Mapping is Small takes the image of $a$ under $A$, where $a$ is small. --Andrew Salmon 19:09, 9 August 2012 (UTC)

$A$ is a class; hence it cannot be a mapping, is then my reply. But I can see how it can be defined, similar to the other things. I still think it a good idea to have a page defining all the derived concepts of $\in$ for classes explicitly. That will ensure that we can refer and prove rigorously. --Lord_Farin 19:11, 9 August 2012 (UTC)

Yes. Nothing need change for any of the definitions--they can all be generalized to classes. --Andrew Salmon 19:13, 9 August 2012 (UTC)

The separate page would be there to expand the difference between $\in$ for classes and for sets. We can't allow referring to $\in$ for classes as were we in naive set theory. That would destroy the whole purpose of foundational mathematics. --Lord_Farin 19:16, 9 August 2012 (UTC)