Date: Oct 19, 2012 12:58 AM
Author: Joe Niederberger
Subject: Re: In favor of teaching "dot notation"

Lou Talman says:
>That's a very good question. How does one handle units in general? What axioms does one use? If there are none, then Robert's earlier question about an exam is well-posed: "Is this mathematics?"

Hmmm, this seems easy to parse, but the options all seem absurd. Is mathematics [A] only that which deduces conclusions from logic, axioms, and rules of inference?
[B] Is it the study of "units"? [C] Is it the study of those two things together? [D] Is it the study of either of those two, together or alone?

Seems ill-posed to me. Please clarify. What exactly are your criteria for including or excluding a topic as mathematics?

Regardless, surely most people reading this board understand that the study of computation is in fact the study of transformations of (finite) symbolic representations by a finite set of well-defined rules. A such it meets criteria A, C, & D always, B sometimes. Axioms that apply include logical axioms and axioms of set theory relevant to finite sets, at minimum.

Here's a starter course:
http://www.spatial.maine.edu/~worboys/processes/hoare%20axiomatic.pdf

This stuff ain't exactly news.

Joe N