On 24 December 2013 16:21, Brian van den Broek <[email protected]> wrote: > On 23 December 2013 13:32, Danny Yoo <[email protected]> wrote: >> >> I've got a puzzle: so there's a well-known function that maps the >> naturals N to N^2: it's called Cantor pairing: >> >> http://en.wikipedia.org/wiki/Pairing_function
<snip> > Hi Danny, > > It does generalize; a well known result of set theory has it that the > Cartesian product of finitely many countable sets is itself countable > (where countable means either finite or infinite but able to be mapped > 1:1 to the natural numbers). Here's a hand-wavy proof sketch that > assumes we've already got the map N -> N^2: <snip me blathering wrongly> Hi Danny and all, What I said was not right. (I cannot now see how I thought it was.) Apologies. For an actual proof: http://planetmath.org/thecartesianproductofafinitenumberofcountablesetsiscountable. Best, Brian vdB _______________________________________________ Tutor maillist - [email protected] To unsubscribe or change subscription options: https://mail.python.org/mailman/listinfo/tutor
