**Title**

The Significance of Distinguishing Functions from Algebraic Equations

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**Summary**

This paper answers the question from a syntax perspective: “*Why is the ‘t’ variable in Einstein’s Tau equation different than the ‘t’ variable in the x’=x-vt equation*“? In answering this question, the concepts of scope, namespaces, global variables, and local variables are introduced.

**Abstract**

The mathematical mistreatment of functions as algebraic equations results in errors that are impossible to detect without a thorough understanding of scope and namespaces. Algebra defines what variables are, how they interact with other variables to form equations, and how multiple equations can be combined or solved as a system of equations. Functions operate in a similar way, but introduce a new layer of complexity due to the abstraction that occurs by separating function definition from function invocation. Here we show that functions are different from algebraic equations and that, under certain circumstances, their mistreatment as an algebraic equation will result in nearly impossible to detect mathematical errors. Explaining these differences will require the introduction of scope and namespaces, which are cornerstone concepts in the proper treatment of functions. Within this context, we explain the differences between optimization and simplification, and between invocation and substitution.

**Status**

- Created: March 2009
- Last Revised: March 2009
- Publication Status: Submitted to Galilean Electrodynamics, March 2009