Whole Numbers

Whole numbers are the foundation of mathematics, representing quantities and order without fractions or decimals. Starting from zero and progressing infinitely, they are essential for counting, measuring, and solving everyday problems.

Table Of Contents

What are whole numbers?
What is the smallest whole number?
Are all natural numbers whole numbers?
Is zero a whole number?
What is the difference between whole numbers and integers?
Do whole numbers include fractions or decimals?
What are the properties of whole numbers?
What is the predecessor of a whole number?
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What are whole numbers?

Whole number ( $\mathbb{N}_\mathbf{0}$ ) includes all non-negative integers: 0, 1, 2, 3, and so on. They encompass zero and all positive integers, excluding negative numbers, fractions, and decimals.

Example: ( $\mathbb{N}_\mathbf{0}$ ) = {0, 1, 2, 3, 4, 5, …}

What is the smallest whole number?

The smallest whole number is 0. Whole number starts from zero and increase by increments of one indefinitely.

Are all natural numbers whole numbers?

Yes, all natural numbers are whole numbers. Natural numbers typically start from 1 and include all positive integers. Since whole number includes zero and all natural numbers, every natural number is also a whole number.

The difference between natural numbers and whole numbers

Is zero a whole number?

Yes, zero is considered a whole number. It begins with zero and includes all positive integers

What is the difference between whole numbers and integers?

Whole number consists of zero and all positive integers (0, 1, 2, 3, …), whereas integers include all positive and negative whole numbers, as well as zero (…, -3, -2, -1, 0, 1, 2, 3, …).

Therefore, integers encompass negative numbers, which whole numbers do not.

Do whole numbers include fractions or decimals?

No, whole number does not include fractions or decimals. They are complete, indivisible units without fractional or decimal components.

What are the properties of whole numbers?

Here are the properties explained with examples:

Closure: The sum or product of any two whole numbers is always a whole number.
Example: ${3}+{5}={8}$ and ${3}\times {5}={15}$
However, subtraction or division of whole numbers may not always result in a whole number.
Example: ${5}-{8}={-2}$ (not a whole number)
Commutative Property: Changing the order of numbers does not change the result for addition or multiplication.
Example: ${a} + {b} = {b} + {a}$ and ${a} \times {b} = {b} \times {a}$
Associative Property: Grouping the numbers does not change the result for addition or multiplication.
Example: $({a} + {b})+{c} = {a} + ({b}+{c})$ and $({a} \times {b}) \times {c} = {a} \times ({b} \times {c})$
Distributive Property: Multiplication distributes over addition.
Example: ${a} \times ({b}+{c})$ = ${a}\times {b} + {a} \times {c}$ .

What is the predecessor of a whole number?

The predecessor of a whole number is the number that comes immediately before it. For any whole number ${n}$ , its predecessor is ${n}-{1}$ . However, zero does not have a predecessor within the set of whole numbers, as there are no negative numbers in this set.