I hope I'm in the right place.

I am no mathematician - just an interested bystander - so please forgive any naivety and stupid questions.

I am going through the sections on Limits & Continuity in Russell's "Introduction To Mathematical Philosophy". One thing that has got me completely stumped at the moment is his definition of the minima of a class with respect to a relation. It goes something like this:

Given 2 classes,a&b, & a relation, P, ona&b, then the minima ofawith respect to P is:

Those members ofaandany members of the field of P (I'll use P.field from now on) that are not related by P froma.

Now "field" as it is used in the book refers to:

a) The domain of the relation

plus

b) The converse domain of the relation

As I understand it the domain in this case is those members ofathat can be mapped by Ptoone or members ofb.

Similarly I understand the converse domain to be those members ofbthat are mappedfromone or more members ofaby P.

The bit that confuses me is the reference to the members of P.field. The way I understand it P.fieldisthe map ofatob, produced by P.

In which case the only members ofain P.field are, by definition, mapped to members ofb, and vice-versa forb.

So how can the minima ofainclude anything in P.field?

Perhaps my conception of "relation" isn't correct? The way I see it is as a map from the domain to the converse domain. e.g. A binary relation ona&bproduces a list ofa,bcouples, a ternary relation ofa's &b's toc's produces a list ofa,b,ctriples.

I'd be grateful if anyone can spot the cause/s of my confusion!