Math Forum: Lee: Lesson 1 - Do it by Functions

Objective:	A function as a black box is promised to do a list of specific tasks. We give input to the black box and then it returns the output, every time we call upon it. A familiar example of function is the washing machine in our homes. We put dirty clothes (input) to a washing machine and out come

	the clean clothes (output). If output of the first washing is not clean enough, you may run the washing machine again by putting dirty clothes back into it as the input for second washing. This is function iteration. Some functions are defined by an equation; the math function. And, others are specified by a list of “to do,” like a washing machine; the word function. We study in detail the math functions of simple doubling and population growth, and word functions of Cantor set and binary tree branching.

Scary words:	Function, input and output, iteration and iterate, binary numbers, fixed point, the Cantor set.

Lesson 1. Do it by Functions