Question

fill in the blank in the sentence below so that the resulting statement is true.

the set \\(\\{..., -4, -3, -2, -1, 0, 1, 2, 3, 4, ...\\}\\) is called the set of ______.

the set \\(\\{..., -4, -3, -2, -1, 0, 1, 2, 3, 4, ...\\}\\) is called the set of

• rational numbers.
• irrational numbers.
• whole numbers.
• integers.

Explanation:

Analyze the given set

The set is written as:

$$ \{\dots, -4, -3, -2, -1, 0, 1, 2, 3, 4, \dots\} $$

This set contains all positive whole numbers, negative whole numbers, and zero.

Evaluate the definitions of the options

We compare the given set with standard mathematical number systems:

• Rational numbers: Numbers that can be written as a fraction \(\frac{a}{b}\) where \(a\) and \(b\) are integers and \(b

eq 0\).

• Irrational numbers: Real numbers that cannot be expressed as a simple fraction (e.g., \(\pi\), \(\sqrt{2}\)).
• Whole numbers: The set of non-negative integers \(\{0, 1, 2, 3, \dots\}\).
• Integers: The set of all positive and negative whole numbers, including zero.

Match the set to the correct term

The set \(\{\dots, -4, -3, -2, -1, 0, 1, 2, 3, 4, \dots\}\) matches the definition of integers.

Answer:

• rational numbers.
• irrational numbers.
• whole numbers.
• integers. (Correct answer)