Eventually or Frequently? The two terms, “eventually” and “frequently,” stood out to me as having fairly interesting definitions when the came up some introductory courses in analysis and toplogy while I was in graduate school. Specifically, I am referring their use in the context of infinite sequences. Now to lay the foundation for the illustration… [Read more…]
December 13, 2005
Discretize Spaces My last entry mentioned that the next post would focus on why I find approximation theory so interesting. I’ve been chewing on an idea / illustration for some time now that I want to run by my readers. Much of my research in has been spent in using finite dimensional function spaces to… [Read more…]
November 30, 2005
A Well Ordering Principle In set theory, we describe a set [tex]X[/tex] as being totally ordered if there exists a binary relation, [tex]\leq[/tex], that is antisymmetric, transitive and total. A binary relation, [tex]\leq[/tex] is antisymmetric if [tex]a\leq b[/tex] and [tex]b \leq a \ \Rightarrow \ a=b[/tex] A binary relation, [tex]\leq[/tex] is transitive if [tex]a \leq… [Read more…]
December 14, 2005
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