What are integers defined as?

• A. Only positive whole numbers
• B. Negative whole numbers only
• C. Natural numbers and their negatives
• D. All rational numbers

Answer: (C)

Integers are defined as the set of whole numbers that include all positive whole numbers, all negative whole numbers, and zero. This definition encompasses natural numbers (which are the positive whole numbers) and their negatives, aligning perfectly with the choice identified.

Natural numbers are 1, 2, 3, and so on, while their negatives are -1, -2, -3, etc. Including zero, the complete set of integers is represented as {..., -3, -2, -1, 0, 1, 2, 3, ...}. This clarity establishes why the selected answer accurately reflects the definition of integers.

The other choices inaccurately limit the scope of integers or mischaracterize their inclusion. Positive whole numbers exclude negative integers and zero, while negative whole numbers do not capture the entire spectrum of integers. Additionally, rational numbers encompass all fractions and decimals, which extends beyond the integer definition. Thus, the correct choice provides a comprehensive view of integers as both natural numbers and their negatives.