I was reviewing relations and functions and I came across the definition serial which is new to me. This more or less throws a wrench in what I thought I understood and I'm seeking clarity.
If I think of this in terms of mapping one ellipse to another, then I understood the left ellipse to be the domain and the right ellipse to be the codomain. The relation mapping the domain to the codomain does not have to cover the full codomain, where the part that it does cover is the image (or range). This is basically a nested ellipse in the codomain, where if the ellipses are the "same", then the relation is surjective.
Going back to my opening acknowledgment with the use of serial, it sounds like there is a nested analog of image for the left ellipse? In other words, to just call the left ellipse the domain is incorrect? There should be "parent-child" ellipses, in which one of them is the domain? Based on the names, intuition says the analog of codomain is domain, but then what is the analog of image?
From what I see in the link above, it sounds like serial means that the left ellipses are the "same", which admittedly is what I assumed all along. If the relation is not serial, then we have a distinction between domain and ?