Business math mid 2nd Sem

1. Classification of Real Numbers
by Kevin Thompson
There are several different subsets of real numbers that either share common properties, fall into
natural groupings, or are viewed as "similar" by mathematicians. There are several different ways to
view the classification of real numbers with some students finding one illustration more helpful than
another.
The chart below shows the subsets in decreasing size (so to speak) from top to bottom. The real
numbers split into two non-overlapping subsets: the rational numbers and the irrational numbers. The
rational numbers contain several nested subsets of simpler and simpler numbers. Examples of numbers
in each subset are given.

2. This second chart is in the form of a Venn Diagram (a chart specifically designed to show sets of
numbers or objects and their intersections and/or nesting). The outside box represents all real numbers.
It is initially split into two non-intersecting subsets: the irrational numbers (the larger of the two) and
the rational numbers. These sets do not overlap and therefore do not share any numbers (all numbers
are either rational or irrational but not both).
The rational numbers contain a number of completely nested subsets. A number in a nested subset
(such as the natural number 1) is a member of all the larger sets that include it (i.e. whole numbers,
integers, rational numbers, and real numbers). An integer such as the number -1 will be a rational
number and a real number but not a whole number.
There are no commonly used subsets of irrational numbers.