Introduction to Integers

Integers, Absolute Value, and Additive Inverse

Rational Numbers

Definition.

The set of rational numbers is the set

Examples:

(a) –5 is a rational number since .

(b) is a rational number since .

(c) –2.15 is a rational number since .

What, if any, are the relationships between the sets of natural numbers (N), whole numbers (W), integers (Z), and rational numbers (Q)?

The Euler diagram (a variation of a Venn diagram) illustrates that there is a subset relationship between the sets.

Self Check Problem

Note that they are proper subsets. Why?

Solution

Joke or Quote

A biologist, a physicist and a mathematician were on a hiking trip in the country. During a rest break, they saw a man and a woman enter a house. Ten minutes later, they reappeared together with a third person.

The biologist stated, "They have multiplied."

The physicist replied, "No, no, there is an error in measurement."

The mathematician confidently stated, "Clearly, if exactly one person enters the building now, the building will be empty."  (–1 + 1 = 0)

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