Definition talk:Well-Defined/Mapping

Formalization

Rigorously, what this means is that $\phi$, provisionally already called 'mapping', is first defined as a relation by assigning to an equivalence class possibly many images. The statement that the relation is well-defined means that the relation $\phi$ is a mapping. --barto (talk) (contribs) 13:01, 24 March 2018 (EDT)

Well-defined mappings in other contexts

Note also that the issue of well-definedness occurs in different settings (i.e. other than quotient sets), and that the above formalization encompasses all those settings. Example: when you want to define a mapping on a vector space or module by representing an element as a linear combination of a generating set (not a basis), i.e. via a not necessarily unique representation. --barto (talk) (contribs) 13:09, 24 March 2018 (EDT)

This page specifically relates to a quotient mapping, though. --prime mover (talk) 13:11, 24 March 2018 (EDT)