Algebra Know-It-ALL

Before going farther with numbers, you should be familiar with sets and the symbols that

describe their behavior. Sets are important in all branches of mathematics, including algebra.

Put on your “abstract thinking cap”!

The Concept of a Set

Aset is a collection or group of things called elements or members. An element of a set can be

anything you can imagine, even another set. Sets, like numbers, are abstractions. If you have a

set of a dozen eggs, you have something more than just the eggs. You have the fact that those

eggs are all in the same group. Maybe you plan to use them to “rustle up” flapjacks for your

ranch hands. Maybe your sister wants to try to hatch chickens from them.

To belong, or not to belong

If you want to call some entity x an element of set A, then you write

x ∈A

The “lazy pitchfork” symbol means “is an element of.” You can also say that x belongs to set

A, or that x is in set A. If some other entity y is not an element of set A, then you can write

that as

y ∉A

An element is a “smallest possible piece” that can exist in any set. You can’t break an element

down into anything smaller and have it remain a legitimate element of the original set. This

little notion becomes important whenever you have a set that contains another set as one of

its elements.

19

CHAPTER

2

The Language of Sets

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