Whole Numbers
Whole numbers are a category of numbers used primarily for counting discrete objects or arranging items in order. Often referred to as natural numbers or counting numbers, whole numbers may include zero, depending on the context. They are defined as numbers that represent whole, indivisible entities, contrasting with divisible objects that can be divided into fractional units. This distinction is crucial in avoiding misinterpretation of statistical data. For instance, when discussing average family sizes, whole numbers provide a clearer representation of the concept, as family members cannot exist in fractions. In statistics, average values can result in non-integer figures, but these averages can be misleading if interpreted literally. Instead, it’s more accurate to describe family sizes using whole numbers to reflect that families consist of complete individuals. Overall, whole numbers serve as a foundational element in various mathematical and real-world applications, offering clarity in counting and arrangement.
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Whole Numbers
If you are counting whole objects in the real world, you are using whole numbers. Whole numbers (mathematical symbol N) can also be called natural numbers or counting numbers. Some people include 0 in the list, and some do not. With or without 0, the fundamental definition of whole numbers is that they are the numbers we use for counting indivisible objects or for arranging ordered items. Indivisible objects either exist fully or fully fail to exist. This is in contrast to divisible objects, which can be apportioned in partial units. Confusion between these qualifications sometimes leads to misinterpretation of important information.
For example, in 1960 the average family in the United States was made up of 3.67 people, and in 2013 the average family in the United States was made up of 3.12 people. Unfortunately, a literal-minded reader would get the impression from these statistics that the average household in the United States has somehow got a family member who is only partly human or part of a human. Of course, this is not what those numbers mean.
The family sizes described as either 3.67 or 3.12 people are averages, calculated in the same way that we can say that the average of 3 and 5 is 4, or the average of 3 and 4 is 3.5. Outside of a statistics-oriented context, a quality like family size should really be described with whole numbers. To do that, we would say that in 2013, the average family in the United States had between 3 and 4 people. This expression is less precise but it is also more accurate.
By comparison, if we were describing the number of apples in the average home, a number like 3.67 would be both precise and accurate. Unlike an indivisible person, an apple can be split into fractions that remain "apple." If a family had 4 apples, and cut 1 of the 4 into 3 equal pieces and gave away one of those pieces, 3.67, or 3 2/3, apples.
Bibliography
Hanna, Gila. Explanation and Proof in Mathematics. New York: Springer, 2014.
McKellar, Danica. Math Doesn’t Suck. New York: Plume, 2008.
Miller, Julie. College Algebra Essentials. New York: McGraw, 2013.