1.1. The Real Numbers

In mathematics, as in many other fields, we must learn many new terms. These definitions will make it easier to talk about mathematical ideas later.

1.1.1. Integers

The integers

..., −4, −3, −2, −1, 0, 1, 2, 3, 4, ...

are the whole numbers, also called the natural numbers or counting numbers, including zero and negative values. The three dots on the ends indicate that the sequence of numbers continues indefinitely in both directions.

1.1.2. Rational and Irrational Numbers

The rational numbers include the integers and all other numbers that can be expressed as the quotient of two integers. Some rational numbers are

Numbers that cannot be expressed as the quotient of two integers are called irrational. Some irrational numbers are

where π is approximately equal to 3.1416 and e is approximately equal to 2.7182. We will have much more to say about the irrational numbers and e later in the book.

1.1.3. Real and Imaginary Numbers

The rational and irrational numbers together make up the real numbers. Numbers such as do not belong to the real number system. They are called imaginary numbers and are discussed in a later chapter. Except when otherwise noted, all the ...

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