On Sat, May 28, Levi Pearson wrote: > > Now, if you want to know a set with a higher cardinality than R, I > can't help you there.
The set of all squiggles on the plane; or, equivalently, the set of all sets of rational numbers. That seems to be the cardinality of the set of all n-dimensional objects, for any finite n (neglecting the physical restraints of elementary particles), and probably the set of points in an infinite-dimensional space. I'm fairly certain that the set of all infinite-dimensional objects is larger still. However, I can't say for sure which cardinality holds the set of all finite-dimensional objects. Blame "Here's Looking at Euclid" for at least part of that line of thought. My wonderful wife picked up a copy for me; it's a very well-written book, interweaving descriptions of several interesting mathematical concepts with the history of various mathematicians who studied them. It makes the point, for example, that the general decline in religion's power over the last few centuries may very well be due to gambling... - Eric /* PLUG: http://plug.org, #utah on irc.freenode.net Unsubscribe: http://plug.org/mailman/options/plug Don't fear the penguin. */
