On 10 March 2018 at 02:18, MRAB <pyt...@mrabarnett.plus.com> wrote: > On 2018-03-10 01:13, Steven D'Aprano wrote: >> >> I am trying to enumerate all the three-tuples (x, y, z) where each of x, >> y, z can range from 1 to ∞ (infinity). >> >> This is clearly unhelpful: >> >> for x in itertools.count(1): >> for y in itertools.count(1): >> for z in itertools.count(1): >> print(x, y, z) >> >> as it never advances beyond x=1, y=1 since the innermost loop never >> finishes. >> >> Georg Cantor to the rescue! (Well, almost...) [...] >> Can anyone help me out here? >> > Think about the totals of each triple. You'll get totals of 3, then totals > of 4, etc. > > This might help, although the order they come out might not be what you > want: > > def triples(): > for total in itertools.count(1): > for i in range(1, total): > for j in range(1, total - i): > yield i, j, total - (i + j)
Mathematically, that's the usual generalisation of Cantor's diagonal argument. Paul -- https://mail.python.org/mailman/listinfo/python-list
