Which set includes integers, including negatives, zero, and positives?

Which set includes integers, including negatives, zero, and positives?

• A. Natural Numbers
• B. Rational Numbers
• C. Integers
• D. Irrational Numbers

Answer: (C)

Integers are all whole numbers, including negatives, zero, and positives. This means numbers like -7, 0, and 12 are integers, and they have no fractional part. Natural numbers are the counting numbers and typically start at 1 (sometimes 0), so they don’t include negative numbers. Irrational numbers cannot be written as a fraction of integers, so they aren’t integers. Rational numbers are numbers that can be expressed as a fraction p/q with integers p and q ≠ 0; this set includes integers as a special case (every integer is a fraction with denominator 1), but the idea described by the term “integers” is the set of numbers with no fractional part. Therefore, the set that matches the description is the integers.

Integers are all whole numbers, including negatives, zero, and positives. This means numbers like -7, 0, and 12 are integers, and they have no fractional part. Natural numbers are the counting numbers and typically start at 1 (sometimes 0), so they don’t include negative numbers. Irrational numbers cannot be written as a fraction of integers, so they aren’t integers. Rational numbers are numbers that can be expressed as a fraction p/q with integers p and q ≠ 0; this set includes integers as a special case (every integer is a fraction with denominator 1), but the idea described by the term “integers” is the set of numbers with no fractional part. Therefore, the set that matches the description is the integers.