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Re: aleph-null versus aleph-one



At 02:00 PM 8/11/00 -0500, Gary Karshner wrote:
The number of point in a line is not countable.

True.

Since between any two successive points, I can find an
infinite number of rational numbered points,

Not true. The rationals are countable. If you can count the whole line of
rationals, you can certainly count an interval full of rationals.

much less irrational ones.

The number of rationals (aleph-null) is indeed much less than the number of
reals (aleph-one).