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Originally posted by Kata
Hmmm.... I have a problem with the satement of "holding the bar at the beginning of infinity" just because if the bar was infinate, then there was not ever a beginning of the pole because the pole spans forever and always has.
Originally posted by Cascadego
Amantine is correct about the bar:
You would be holding the bar at or near the beginning of an infinity.
As to the cardinality of the number line:
All positive-integers are countable (aka aleph 0 or whatever notation he is using)
card(pos. and neg. integers) = card(pos. integers)
card(all rationals, +and-) = card(pos.integers)
card(irrationals) not countable (aka aleph1)
the union of two countable sets is still countable.. blah blah
but the 2^aleph0 thing i seriously doubt, unless i am wrong in my assumption that aleph1 is the uncountablt infinity we discuss in our transfinite courses here at ucb.
The reason is that the cartesian space has the same cardinality as the number line. And if you constrain your cartesian space to include only rational numbers, then even an infinite dimensional space still only contains a countable infinity of points.
Originally posted by amantine
aleph0^aleph0 = c
Originally posted by quiksilver
maybe he is referring to physical things, but will we ever know without refferng to mathematics? because i doubt we can actually observe and identify an infinity without referring to mathematics(because you cant measure an infinity)
Originally posted by TheBandit795
(...)
If you traveled a straight line in those dimensions, you will eventually reach back to the exact place you first were.
(...)
Originally posted by Faceless
One more question:
10 / 3 = 3.333333333.... going on for infinity.
How can that be? If there are 3's for infinity wouldn't they all add up to be infinity and not 10?