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 (xA) ↔ (xB).
  • A and B are diverse if this is not the case; that is, there is an x with either (xA) but not (xB), or (xB) but not (xA). This used to be called “inequality”, but the term is now deprecated.
  • A includes B if, for all x, we have (xB) → (xA). 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.

About Peter Cameron

I count all the things that need to be counted.
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5 Responses to EDI

  1. I suppose the difficulty is that although it is easy to define `binary’, it is not so easy to define `non-binary’ if there is no universal agreement about a universal set.

  2. Allan van Hulst says:

    Recently I learned that equality can be achieved via repeated cancellation and that this method is both necessary and sufficient. It therefore seems possible to define equality in a unary fashion until a critical part remains on the left and the right hand side is empty.

  3. DQ says:

    Please don’t destroy your lectures notes so as to avoid “subset”.

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