EDI

We hear a lot about equality, diversity and inclusion now. Perhaps it would be good to remind ourselves of the formal definition.

• A and B are equal if, for all x, we have (x∈A)  (x∈B).
• A and B are diverse if this is not the case; that is, there is an x with either (x∈A) but not (x∈B), or (x∈B) but not (x∈A). This used to be called “inequality”, but the term is now deprecated.
• A includes B if, for all x, we have (x∈B) → (x∈A). The older terms “subset” and “superset” have overtones of class and should be avoided.

Please note that all the above are binary. This is an obvious shortcoming: there is a high-level commission of logicians working on a non-binary version, but it is proving to be a challenging problem.