The set of whole numbers refers to a collection of numbers that includes all positive integers along with the number zero. In mathematical terms, whole numbers can be represented as:
Whole Numbers = {0, 1, 2, 3, 4, 5, …}
Here, you can see that the whole numbers start at zero and continue infinitely in the positive direction. They are non-negative numbers that do not include any fractions or negative values.
On the other hand, positive integers are a subset of whole numbers and are defined as:
Positive Integers = {1, 2, 3, 4, 5, …}
This set starts from one and goes upwards into infinity, essentially omitting zero. Thus, while all positive integers are whole numbers, not all whole numbers are positive integers since whole numbers include zero as well.
Understanding this distinction is crucial in various mathematical contexts, especially when dealing with concepts of counting, representation of quantities, and number theory. The inclusion of zero in the whole numbers also plays an important role in different operations and functions in mathematics.