Whole numbers and integers are both fundamental concepts in mathematics, and while they may seem similar at first glance, they have distinct definitions that set them apart.
Understanding Whole Numbers
Whole numbers are defined as the set of non-negative numbers that do not include any fractions or decimals. This set includes:
- 0
- 1
- 2
- 3
- 4
- 5
- …
Essentially, whole numbers start from zero and go on infinitely in the positive direction.
Understanding Integers
Integers, on the other hand, include both positive and negative whole numbers, as well as zero. The set of integers is represented as:
- …, -3
- -2
- -1
- 0
- 1
- 2
- 3
This means that integers extend infinitely in both the negative and positive directions, encompassing all whole numbers and their negative counterparts.
The Key Differences
- Negative Numbers: Whole numbers do not include any negative numbers, while integers do.
- Starting Point: Whole numbers start from zero, whereas integers can be positive, negative, or zero.
- Sets: The whole number set is a subset of the integer set. This means every whole number is an integer, but not every integer is a whole number.
In summary, the most significant difference lies in the inclusion of negative numbers; whole numbers are only non-negative, whereas integers encompass all whole numbers, both positive and negative, along with zero.