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Old 21st February 2003, 07:09 PM   #11
mirlo is offline mirlo  United States
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Default Continuum Hypothesis and Axiom of Choice

Actually, the continuum hypothesis, ie the statement that there is no infinite set larger than the integers and smaller than the real numbers, doesn't depend accepting or rejecting the axiom of choice, but is independent. It makes for some interesting reading.

http://www.ii.com/math/ch/
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Old 21st February 2003, 07:26 PM   #12
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I always thought "the sciences" were just sub-sets of physics, and physics just a sub-set of applied math.

Dad used to tell me, "If ya can't graph it, ya don't understand it!"

Cyclotronguy/ takes comfort in numbers
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Old 21st February 2003, 08:06 PM   #13
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Default Re: Continuum Hypothesis and Axiom of Choice

Quote:
Originally posted by mirlo
Actually, the continuum hypothesis, ie the statement that there is no infinite set larger than the integers and smaller than the real numbers, doesn't depend accepting or rejecting the axiom of choice, but is independent. It makes for some interesting reading.

http://www.ii.com/math/ch/
You are right of course; it's been way too long since
I'd studied this stuff.

Dennis
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Old 21st February 2003, 08:36 PM   #14
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I don't know anything about descrete math or advanced physics,
but I can ad to the "origin of Aleph" discussion that Aleph is also the first letter in the Fenician ( the ancient ancestors of the egyptions ) alfabet. And if I remember correctly it meant Ox.

/Chris
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Old 21st February 2003, 09:18 PM   #15
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Yes, Aleph is the first letter of the Hebrew alphabet.
It has the meaning of ox and in tarot it corresponds to
The Fool. It corresponds to the primal energy, spirit and
to the element of air. It also indicates limitless possibilities.
And many other things besides. An ox is a motive force.
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Old 21st February 2003, 10:29 PM   #16
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Nelson was fascinated by the works of Georg Cantor, a mathematician who spent his last years in an asylum contemplating the mathematical meaning of infinite.


Cyclotronguy
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