On Fri, May 27, 2011 at 02:52:21PM -0600, Daniel C. wrote: > > No. I meant to say exactly what I said - that there are in fact > "more" numbers between 0-2 than there are between 0-1. That is, the > cardinality of the set of all numbers between zero and one is of a > lower order than the cardinality of the set of all numbers between > zero and two. However, since neither of these sets are countable, the > concept or "more" or "less" (which applies just fine to finite sets - > iirc, all finite sets are countable) breaks down when talking about > infinite sets, especially ones that are uncountable.
The cardinality of the interval (0, 2) is the same as the cardinality of the interval (0, 1). The definition of cardinality is well-defined for both finite and infinite sets: if there's a bijective (one-to-one and onto) function from one set to another, then the two sets have the same cardinality. However, the measure of the interval (0, 2) is greater than the measure of the interval (0, 1), which might be what you're trying to get at. This conversation is incredibly difficult to follow because everyone is mixing up natural numbers and real numbers; cardinality and measure; etc. I don't even get what point anyone is trying to make. :) -- Andrew McNabb http://www.mcnabbs.org/andrew/ PGP Fingerprint: 8A17 B57C 6879 1863 DE55 8012 AB4D 6098 8826 6868 /* PLUG: http://plug.org, #utah on irc.freenode.net Unsubscribe: http://plug.org/mailman/options/plug Don't fear the penguin. */
