Yes, the canonical example is that there are more real numbers than natural numbers. The natural numbers have the smallest transfinite cardinality. On May 28, 2011 2:15 AM, "Daniel C." <[email protected]> wrote: > On Sat, May 28, 2011 at 2:10 AM, Levi Pearson <[email protected]> wrote: >> Anyway, after a bit more research, I found that you can use the arctan >> and tan functions to map between R and any open interval within R, >> which does prove that Daniel was wrong and the two sets he mentioned >> were in fact the same size. In fact, since 0..1 is a subset of 0..2, >> the elements map with the identify function, and you can map 0..2 back >> into 0..1 by dividing each element in the set by 2. Easy! >> >> Now, if you want to know a set with a higher cardinality than R, I >> can't help you there. > > Bad example aside, am I correct in thinking that there are different > infinities, some of which "have more things in them" (a higher > cardinality) than others? > > /* > PLUG: http://plug.org, #utah on irc.freenode.net > Unsubscribe: http://plug.org/mailman/options/plug > Don't fear the penguin. > */
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