Whole number

Definition

A whole number is a non-negative integer that does not include any fractions or decimals. Whole numbers start from zero and continue indefinitely, encompassing all the positive integers and zero, making them foundational in mathematics. Understanding whole numbers is crucial for basic arithmetic operations like addition, subtraction, multiplication, and division.

5 Must Know Facts For Your Next Test

1. Whole numbers include 0, 1, 2, 3, and so on, extending infinitely in the positive direction.
2. Whole numbers are closed under addition and multiplication, meaning that adding or multiplying whole numbers will always result in another whole number.
3. The set of whole numbers is often denoted by the symbol ℕ₀, which signifies the inclusion of zero.
4. When performing operations with whole numbers, you never deal with fractions or decimal points.
5. Understanding whole numbers is essential for higher-level math concepts and operations since they serve as the building blocks for more complex numerical systems.

Review Questions

• How do whole numbers differ from integers and natural numbers in terms of their definitions and applications?
  • Whole numbers differ from integers primarily in that they do not include negative numbers; they consist of all non-negative numbers including zero. In contrast, natural numbers exclude zero and begin from one, only comprising positive integers. This distinction is important because it influences how we apply these number sets in arithmetic operations and real-life situations, such as counting objects where natural numbers would be more appropriate.
• Explain how the properties of whole numbers support their use in basic arithmetic operations like addition and multiplication.
  • The properties of whole numbers, such as closure under addition and multiplication, support their use in basic arithmetic by ensuring that the results of these operations will always yield whole numbers. For instance, if you add two whole numbers together or multiply them, you will never encounter a fraction or decimal in the result. This reliability makes them ideal for counting scenarios and basic calculations where precision in whole quantities is essential.
• Assess the significance of understanding whole numbers in relation to advanced mathematical concepts and their practical applications.
  • Understanding whole numbers is crucial because they form the foundation for more advanced mathematical concepts such as algebra and calculus. They are involved in various real-world applications, from financial transactions to statistical analysis. As students progress in their education, a solid grasp of whole numbers enables them to tackle more complex problems efficiently and understand abstract concepts that rely on numerical foundations. This foundational knowledge directly impacts their ability to engage with mathematics critically and creatively.

Related terms

integer: An integer is a whole number that can be positive, negative, or zero, but it does not include fractions or decimals.

natural number: Natural numbers are the set of positive whole numbers starting from one, often used for counting.

rational number: A rational number is any number that can be expressed as the quotient of two integers, where the denominator is not zero, which includes whole numbers.