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I think the idea is roughly this: each packing pattern is represented by an infinite string over the alphabet {a,b,c} that has no doubled letters. And there is
by robinhouston 15y ago
I think the idea is roughly this: each packing pattern is represented by an infinite string over the alphabet {a,b,c} that has no doubled letters. And there is an uncountable infinity of such strings – continuum many – because these strings are in one-one correspondence with infinite binary strings: there are two possibilities for each letter, because it can’t be the same as its predecessor but it can be either of the other two.
- evincarofautumn 15y agoI considered that, then I figured it was reasonable to discount infinitely large pieces of ice.
- leif 15y agoIn that case the number of ice configurations would be finite, not countably infinite. EDIT: lest someone believe me, this is NOT TRUE, the parent is completely right