On 12/6/12, Adam P. Goucher <apgoucher@gmx.com> wrote:
The limit of the series is the *ordinal* omega. You're only allowed to use aleph-null to refer to the sizes of sets.
Thanks for the pedantry Adam, this is math and we need the precision. I am one of the many sufferers of George Gamow's over-simplifications (or some would say outright falsehoods) such as this howler: http://mrob.com/pub/math/images/gamow-123i-p23-fig8.jpg Aleph_1 is identified as "the number of all geometrical points on a line", and the caption called Aleph_0, Aleph_1 and Aleph_2 "the first three infinite numbers" (which implies there are no other infinite numbers in between).
Yes, this is one of those things which are obviously false but actually true. Then there are things which are obviously either true or false, but turn out to be equivalent to the continuum hypothesis instead.
I suppose that's what got Gamow. -- Robert Munafo -- mrob.com Follow me at: gplus.to/mrob - fb.com/mrob27 - twitter.com/mrob_27 - mrob27.wordpress.com - youtube.com/user/mrob143 - rilybot.blogspot.com