Wednesday, June 15, 2011

GDC Vault and Relations

Apparently you can get a lot of the GDC presentations for free at the GDC Vault website.  It doesn't have everything unfortunately (I couldn't find Erin Catto's 2006 presentation), but there are some cool things in there.  I didn't have much time to browse around, but the Halo: Reach networking presentation caught my eye; it's rather good, and I recommend it to anyone who is writing networking code.

Today I learned about relations and Cartesian products.  The Cartesian product of two sets A and B is the set consisting of all the ordered pairs (a, b) where a is an element of A and b is an element of B.

A relation of a set V is any subset of the Cartesian product of V with itself.  Given an ordered pair (a, b) of a relation R, a is said to related to b by R.

Relations can have several properties: reflexive, irreflexive, symmetric, asymmetric, and transitive.  A relation R on V is reflexive if for every x in V there is an element (x, x) in R; it is irreflexive if for every x in V there is no element (x, x) in R.  A relation R is symmetric if for every element (a, b), there is another element (b, a); it is asymmetric if for every element (a, b) where b is not a, there is no element (b, a).  And finally, a relation R is transitive if for every element (a, b) there is an element (b, c) and (a, c).

I also learned that the cardinality of a set is the number of elements in that set.

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