What is `Finite’?

What does `finite’ mean, mathematically?

In February I talked about this in our Lunch Colloquium; you can read the slides of that talk here.
Some time later the editors of Machazine, the journal of our student association Christiaan Huygens, asked me to write something `mathematical’ for them. I decided to expand my talk into a short article for them, it is available here, for your edification.

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