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Re: countable and uncountable



At 10:34 AM 8/11/00 -0700, Bernard G. Cleyet & Nancy Ann Seese wrote:

I thought to count was to put into one to one correspondence with what
one is counting using the integers.

Yes, that's the technical definition of "countable".

This means that there are countable infinities and non countable (de and
undenumerable?).

Of course.

e. gratia. the integers are obviously countable

Yes, practically by definition.

as are the points on a line

Sorry, the points on the real line are uncountable.

-- however the points on a plane are not.

Agreed, points in the plane are not countable.

-- 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,

You seem to be suffering from a memoroid -- something that seems like
memory but isn't.

The points in the plane can be put into 1-to-1 correspondence with the
points in the line. A fellow named Peano had something to say about this.