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Applied Discrete Structures

Chapter 7 Functions and Probablity

countably infinite

A countably infinite set
Is as simple as things like this get.
Just start counting at 1,
Then continue—it’s fun!
I’ll check back when you’re done, so don’t sweat.
Chris Doyle, The Omnificent English Dictionary In Limerick Form
In this chapter we will consider some basic concepts of the relations that are called functions. A large variety of mathematical ideas and applications can be more completely understood when expressed through the function concept.
In addition we will introduce some basic probability theory. This applies some of the basic counting tools we have introduced and will be useful in subsequent chapters. We start by defining finite probability distributions, random variables and their expected value. We then introduce binomial processes, which we use to model random noise in our study of coding theory.