Profile

unixronin: Galen the technomage, from Babylon 5: Crusade (Default)
Unixronin

December 2012

S M T W T F S
      1
2345678
9101112131415
16171819202122
23242526272829
3031     

Most Popular Tags

Expand Cut Tags

No cut tags
Thursday, May 18th, 2006 08:29 am (UTC)
To be a little bit more precise (sorry, this is one of my favorite topics). N (the natural numbers), Z (the integers), and Q (the rational numbers) are all the same size (countably infinite, with cardinality aleph0. R (the real numbers) cannot be put into one-to-one correspondence with any countably infinite set (Cantor originally used N): instead they have cardinality c,1 the name of which is derived from "continuum."2 Note that the set of reals between 0 and 1 -- that is, the open interval set (0,1) -- has the same cardinality as R, which is somewhat interesting. I leave finding a mapping from R to (0,1) to the reader.


1: The Continuum Hypothesis would state that c = aleph1 = 2aleph0.
2: This is how we got into the Continuum Hypothesis and transfinite set theory (which Hilbert called the "paradise of the infinite").

Reply

This account has disabled anonymous posting.
(will be screened if not validated)
If you don't have an account you can create one now.
HTML doesn't work in the subject.
More info about formatting

If you are unable to use this captcha for any reason, please contact us by email at support@dreamwidth.org