Whole Numbers

Definition

Whole numbers are a set of numbers that include all natural numbers along with zero. They are non-negative integers, which means they do not include fractions, decimals, or negative values. This set is foundational in mathematics as it forms the basis for counting and ordering in various numerical contexts.

5 Must Know Facts For Your Next Test

1. Whole numbers start from 0 and go infinitely (0, 1, 2, 3,...), making them a critical part of basic arithmetic.
2. The set of whole numbers is closed under addition and multiplication; this means that adding or multiplying two whole numbers always results in another whole number.
3. Whole numbers do not include negative numbers or any fractions/decimals, which distinguishes them from integers.
4. When plotting whole numbers on a number line, they occupy discrete points that are evenly spaced apart, with zero at the origin.
5. Whole numbers play an essential role in various mathematical operations and are often used in real-life situations like counting objects.

Review Questions

• How do whole numbers differ from natural numbers and integers in terms of their definitions and examples?
  • Whole numbers include all natural numbers starting from 0 (0, 1, 2, 3,...), while natural numbers begin from 1 and do not include zero. Integers encompass both whole numbers and their negative counterparts, such as -1, -2, etc. This distinction is crucial as it impacts how each set is used in mathematical operations and real-world applications.
• What properties do whole numbers exhibit under addition and multiplication, and how does this impact their use in mathematics?
  • Whole numbers are closed under both addition and multiplication, meaning that when you add or multiply any two whole numbers, the result will always be another whole number. This property makes them reliable for computations in basic arithmetic and helps maintain consistency in calculations involving counting or grouping items.
• Evaluate the importance of whole numbers in mathematical concepts and real-life applications by providing examples.
  • Whole numbers are foundational in mathematics because they serve as the building blocks for more complex concepts like algebra and number theory. In real life, we use whole numbers for counting items such as apples in a basket or people in a room. Their simplicity makes them crucial for understanding more complicated mathematical ideas while ensuring clear communication about quantities without ambiguity.

Related terms

Natural Numbers: Natural numbers are the set of positive integers starting from 1 and going upward (1, 2, 3,...), used primarily for counting.

Integers: Integers are a set of numbers that include whole numbers and their negative counterparts, representing both positive and negative values, along with zero.

Rational Numbers: Rational numbers are numbers that can be expressed as the quotient of two integers, where the denominator is not zero, including fractions and whole numbers.