[Python-Dev] PEP 276 (simple iterator for ints) (original) (raw)

Gareth McCaughan gmccaughan at synaptics-uk.com
Thu Jul 1 04:01:39 EDT 2004

On Thursday 2004-07-01 03:17, Greg Ewing wrote:

I suspect most people other than number theorists would find the concept of a set of integers being contained in another integer quite wierd.

Actually, most number theorists would too. It's only set theorists to whom that seems like a natural definition. And the first (so far as I know) attempt to define the natural numbers set-theoretically did it quite differently: Gottlob Frege proposed to define n as the set of all sets of size n. Unfortunately, Frege's version of set theory famously didn't work (it was demolished by Russell's paradox) and his construction doesn't work in ZF set theory, which is what most set theorists use nowadays.

In any case, saying that (e.g.) 3 is a member of 17 is generally regarded as an implementation detail. Mathematicians understand the different between interface and implementation just about as well as software people. (Which is to say: some understand it very well, and others don't.)

By the by, I don't think it's true that sets.Set(42) would, under PEP276, be the usual implementation of 42 in set theory. It would be a set whose elements are ordinary Python integers, which are not themselves sets. If you see what I mean. :-)

-- g

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