The point is that (switching out of metaphor language) you can view 1 as the property of one-ness, or rather being singleton sets. And 2 would thus be the property of having cardinality (=fancyspeak for size) 2, et.c.
Addition might work - with "having size" replaced by "having size at least" - like follows: 1 + 1 = {x union y : x in 1, y in 1} Then you would get some member sets in 1+1 having cardinality 1, but you would most certainly get a lot of member sets having cardinality 2. And so on.
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Date: 2007-09-17 11:18 pm (UTC)Addition might work - with "having size" replaced by "having size at least" - like follows:
1 + 1 = {x union y : x in 1, y in 1}
Then you would get some member sets in 1+1 having cardinality 1, but you would most certainly get a lot of member sets having cardinality 2. And so on.