Understanding Number Sets

To identify the correct set containing the numbers -5, 0, and 6, let's review the definitions of the given options:

• Natural Numbers: These are the positive counting numbers starting from 1. Example: {1, 2, 3, ...}.
• Whole Numbers: These include all natural numbers plus zero. Example: {0, 1, 2, 3, ...}.
• Integers: This set includes all whole numbers (positive numbers, zero) and their negative counterparts. Example: {..., -3, -2, -1, 0, 1, 2, 3, ...}.
• Irrational Numbers: These are numbers that cannot be expressed as a simple fraction, often having non-repeating, non-terminating decimal expansions. Example: $\pi$, $\sqrt{2}$.

Analyzing the Given Numbers

The question asks which set includes the specific numbers -5, 0, and 6.

• -5 is a negative number.
• 0 is zero.
• 6 is a positive number.

Matching Numbers to the Integer Set

Let's check if these numbers fit into the definitions:

• Natural Numbers do not include 0 or negative numbers like -5.
• Whole Numbers include 0 and positive numbers like 6, but not negative numbers like -5.
• Integers include all negative numbers (like -5), zero (0), and all positive numbers (like 6).
• Irrational Numbers are a different category and do not typically include simple integers like -5, 0, or 6 unless specified in a broader context not implied here.

Therefore, the set that comprehensively includes -5, 0, and 6 is the set of Integers.