Number Systems
| Counting Numbers (N) (sometimes called Natural Numbers) |
The Counting Numbers are the positive numbers that do not contain fractions. |
| Examples: | N = {1, 2, 3…} |
| Whole Numbers (W) | The Whole Numbers are 0 and the positive numbers that do not contain fractions (the Counting Numbers and 0). |
| Examples: | W = {0, 1, 2, 3…} |
| Integers (Z) | The Integers are the positive and negative Whole Numbers, including 0 (the Whole Numbers and their opposites). |
| Examples: | Z = {…–3, –2, –1, 0, 1, 2, 3…} |
| Rational Numbers (Q) | The Rational Numbers have the form a/b, where a and b are whole numbers and b ≠ 0, that is, they are all the numbers that can be written as fractions (as ratios). All the Rational Numbers can be written as common fractions, as decimal fractions, and as percents. The decimal form of a Rational Number is either a repeating decimal or a terminating decimal. |
| Examples: | ¼ = 0.25 = 25% ; 1/3 = 0.33... = 33 1/3 % |
| Irrational Numbers (I) | The Irrational Numbers are numbers that cannot be written as a fraction. Their decimal representations do not repeat and do not terminate. |
| Examples: | π = 3.14159... ; √2 = 1.414213... ; x = 0.010010001... |
| Real Numbers (R) | The Real Numbers are all of the Rational and Irrational Numbers taken together. |
| Examples: | All of the above. |
| Complex Numbers (C) | The Complex Numbers (also called Imaginary Numbers) are all the Real Numbers and the numbers that involve the square root of negative one (i) Complex Numbers have the general form a + bi, where a and b are real numbers and i = √-1 |
| Examples: | All of the above (b = 0), and 3 + 2i, 5 – 6i (b ≠ 0). |
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