Fundamentals of Math - old

Fundamentals of Mathematics

Figure 1.2.2 Number Classification

Name

Consists Of

Symbol

Examples

ℕ

Natural

The counting numbers

5, 27, 134, 2641

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Whole

Natural numbers and zero

0, 1, 2, 3, 4

ℤ

Integer

Natural numbers, zero, and opposite natural numbers

−5, −1, 0, 2, 4

Natural numbers, zero, opposite natural numbers, and any number that results in a finite decimal or a repeating decimal.

1 2

7 9

ℚ

Rational

−3, 0,

,

, 7.5

4 23

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Irrational

Non-repeating and non-terminating decimals

, √2, ℮,

ℝ

Real

All rational and irrational numbers

Any number

Now let's look at the second sentence in our definition: Collectively, these values can be represented as a distance along a line.

We organize Real numbers on a straight line with values placed in equal segments along its length; this line, known as a number line , can be extended infinitely in any direction. Values are placed numerically left to right with smaller quantities on the left and extending to larger quantities on the right.

Figure 1.2.3 A Generic Number Line

There is no set number line because a number line is just a visual tool to help users compare values and carry out operations like addition, subtraction, multiplication, and division.

Figure 1.2.4 Types of Number Line

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