This page defined
countable to mean "countably infinite". I've changed this, because in my experience it usually means "countably infinite or finite" (i.e., the opposite of
uncountable). Note that we already have an article on
countably infinite, so there is some duplication here.
Zundark 2001-08-12
This page address cardinals, but what does it mean to say an ordinal is countable or uncountable?
A countable ordinal is just an ordinal which is countable as a set, i.e. its cardinal is aleph_0.
An uncountable ordinal is an ordinal which is not finite and not countable (as a set).
--
AV
Why would we prove the countability of
Q by taking it as a countable union of countable sets? The usual way is just to present an ordering, and is much simpler, IMO.
0, 1, -1, 2, -2, 1/2, -1/2, 3, -3, 1/3, -1/3, 4, -4, 5, -5, 1/5, -1/5, 6, -6, 3/2, -3/2, 2/3, -2/3, 1/6, -1/6, ...
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