## Posts

Showing posts from December, 2005

### The Logic of Space part III

Ok, so last time we left off with a very informal discussion about Venn diagrams and how they relate to Boolean Logic.

First let us do a little set theory and then we'll start drawing connections with the previous post to make it a bit more rigorous. We will stick with completely finite sets, so keep that in mind.

A set is basically a collection of distinguishable objects. Sets have no notion of the number of times an object is in them. They simply contain an object or they do not. A set (if it is finite) can be writen in terms of its elements, for instance: S = {a,b,c} is the set S with elements a,b and c.

A map can be thought of as arrows that leave from one set (the domain) and arive at another (the codomain).

We will also introduce a special set 2^S which is an exponential or a "homset" called hom(S,2). S will be jus t a collection of elements as above, and 2 will be a collection of the elements {0,1}. We can think of a homset as a collection of all maps fro…

### The Logic of Space Part II

I was checking my access logs and noticed that I was #1 on MSN for "logic of space" which is a bit embarassing since my last post had so little content, so I've decided to make it up to those who end up here.