Set Theory and F# with Louis Thrall

Doors open at 6:30, talk begins at 7:00.

Sign in at the desk on the first floor. Make sure you have a valid ID, they won't allow entry without it. The meetup is on the 67th floor.

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What is Set Theory:

ZFC set theory is an axiomatic theory of sets. The reason for such a theory is that one wants a "definition" of what a set is. The reason that sets are important to mathematics is that they provide an encoding of most of mathematics (there are a couple of reasons why one cannot encode all of math).

Why Learn about Set Theory:

Axiomatic set theories provide the theoretical underpinnings of various subjects of interest to programmers and computer scientists. For instance relational database theory. Moreover Lisp/scheme programmers very often use set theoretic notions (I would argue that Lisp/Scheme are in fact founded in set theory). ZFC set theory in particular acts as an assembly language for most of mathematics. Moreover, the central philosophical idea that comes out of set theory is that one may take a collection of objects (not necessarily OPP objects) and treat them as unitary objects. It is also interesting to note the quite a few of the axioms of ZFC come naturally out of common functional constructs such as Append, Filter, and Map.

What I will be Discussing:

In this talk, I will discuss the theory of ZFC set theory, it's raison d'etre (to be pretentious), as well as some applications (time permitting). Some F# code will also be shown that illustrates the axioms of ZFC.

Optional Preparation:

Listen to the Functional Geekery Podcast: http://www.functionalgeekery.com/episode-37-eric-smith/

While he does not mention set theory by name, Set theory is in fact part of the history that he speaks about.