FoundAround 2008-20

Some miscellanea encountered this week:

  • Finite infinite cardinality. There’s a somewhat odd thread over on the XKCD forums about the cardinality of infinite sets. The original poster has an intuitive problem with the fact that an infinite set X may have the same cardinality as a proper subset of X—which is one way of defining what it means for a set to be infinite in the first place. The thread attempts to correct the counterintuitive result by proposing that we take A \subset B \Rightarrow \left|A\right| < \left|B\right| as an axiom. I guess we should just ignore those infinte sets after all?
  • Projectile nonsense. Over at Language Log, a commenter suggested that projectile nonsense may be a subfield of abstract nonsense. I don’t have any good idea what additional axioms we would add to category theory in order to get to this new theory. I have even less of an idea how the chair of a Presidential campaign would go about turning it into “something approaching the sublime”.

Copyright © 2008 Michael L. McCliment.

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