On Sat, May 28, 2011 at 1:41 PM, Andrew McNabb <[email protected]> wrote: > On Sat, May 28, 2011 at 12:37:40PM -0600, Nicholas Leippe wrote: >> >> What about subsets of the natural numbers such as all even numbers, >> fibonacci series, or prime numbers? >> How does the "infiteness" of these kinds of sets get classified? > > They all have the same cardinality as the natural numbers in general. > You can make a list of the first prime number, the second prime number, > etc. This infinite list is a one-to-one and onto function from the > natural numbers to the prime numbers (proof not included in this email), > so the two sets have the same cardinality.
That is extremely counter-intuitive to me. The way I've been looking at it is by starting with the set of all natural numbers, yielding cardinality X, then removing from that set any number that doesn't belong in the other set (such as not prime, or not even, or not fibonacci) until the resultant set is achieved--and it *seems* like that would be fewer numbers and thus the cardinality would be less than X. Just taking the set of even numbers, for example, why isn't the cardinality of that set 1/2 the cardinality of all natural numbers? /* PLUG: http://plug.org, #utah on irc.freenode.net Unsubscribe: http://plug.org/mailman/options/plug Don't fear the penguin. */
