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  • ...divided between those which are [[finite]] and those which are countably [[infinite]]. The name "countable" arises because the countably infinite sets are exactly those which can be put into [[bijection]] with the [[natur
    773 bytes (126 words) - 20:35, 26 September 2008
  • ...every set that is ''not'' uncountable is either [[finite]] or [[countably infinite]]. The most common example of an uncountable set is the set of [[real numb * [[Infinite]]
    2 KB (403 words) - 19:53, 13 October 2019
  • ...Students who know induction can replicate these proofs for the countably infinite case. I simply stick with "ABCDEF is a 6-digit number" and construct a pro
    745 bytes (125 words) - 02:02, 10 May 2016
  • ...nfinite [[convergent]] subsequence. (In fact, we may even ensure that this infinite convergent subsequence converges arbitrarily quickly, but this is beside th ...iterating this construction countably infinitely many times, we obtain an infinite sequence of closed bounded regions <math>K_n</math>, each of which is half
    1 KB (235 words) - 12:25, 29 August 2020