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I thought to count was to put into one to one correspondence with what
one is counting using the integers.
This means that there are countable infinities and non countable (de and
undenumerable?).
e. gratia. the integers are obviously countable
as are the points on a line
-- however the points on a plane are not.
-- the integers are used up just counting the points on one of the
infinite lines that comprise the plane. This is all from G.G 1, 2, 3
Infinity read ca. 1955 He calls these infinities Aleph zero , one, two, etc.
Hope my mem. serves,