Re: Antonelli’s Logicism

[bill taylor]

“There are at least as many B as A” or “There is an injection of A into B”
or “|A|<=|B|”.

>>>> My main objection is that in English there is not a nicely simple
> way to SAY this.
>

 How about "the Bs outnumber the As"; where we would be using the common
math convention
that definitions include their limiting cases, e.g. all squares are
rectangles.

As usual, one may say "strictly outnumbers" if one means _that_.

If one feels "outnumber" has too fixed a meaning, (that being strictly), in
everyday English,
one might create a new word "overnumbers" to do the job.  This would also
seem to cover
the case where the As and Bs are equinumerous, in that "overnumber"
suggests that any
surjection be included - though this "suggestion" might run into the
problem that
a surjection may not be reversible to an injection without the use of AC.

- Bill Taylor
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