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The importance of numbers in mathematics and everyday life is undeniable. From natural numbers used for counting to imaginary numbers for complex calculations, each set plays a critical role. Natural numbers (ℕ) and whole numbers (ℤ⁺ or ℕ₀) are foundational for basic arithmetic. Integers (ℤ) include negative numbers, while rational numbers (ℚ) can be expressed as fractions. Irrational numbers (ℝ\ℚ) have non-repeating decimals, and real numbers (ℝ) encompass all number types. Imaginary numbers extend the system for advanced math and science.

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## Natural Numbers

### Definition of Natural Numbers

Natural numbers are positive integers without zero, used for counting and ordering

### Whole Numbers

Definition of Whole Numbers

Whole numbers include all natural numbers along with zero, and can be visualized on a number line

### Orderly Sequence

Natural and whole numbers can be represented on a number line to show their orderly sequence

## Integers

### Definition of Integers

Integers include all natural numbers, their negative counterparts, and zero, and can be depicted on a number line extending infinitely in both directions

### Classification

Integers provide a more extensive classification that incorporates natural and whole numbers, as well as negative numbers

### Use in Mathematics

Integers are used in various mathematical applications, such as problem-solving in science and engineering

## Rational Numbers

### Definition of Rational Numbers

Rational numbers can be expressed as a ratio of two integers, including integers, proper and improper fractions, and decimals

### Examples

Examples of rational numbers include -5.5, -3/2, 0, 1/2, and 0.75

### Conversion

Decimals can be converted into fractions to show their rational nature

## Real Numbers

### Definition of Real Numbers

Real numbers include all rational and irrational numbers and are used to measure continuous quantities in the physical world

### Use in Daily Life

Real numbers are the most commonly used numbers in daily life and in mathematical applications

### Range

Real numbers cover a broad spectrum, from negative to positive, including zero, fractions, and irrational numbers