All real numbers are classified into different number sets. Within the category of real numbers, we have the following subsets of numbers.
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-3pt Type of& [-0.5em] Number & & Number Set -5pt [0.4em]
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-3pt Whole& [-0.5em] Numbers & & -3pt { ,1,2, ... } -3pt [0.4em]
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Integers & -3pt { ..., -1, ,1,2, ...} -3pt [0.4em]
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-3pt Rational& [-0.5em] Numbers & & -3pt { ..., - 32,-1, ,1,2, ...} -3pt [0.6em]
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-3pt Real& [-0.5em] Numbers & & -3pt { ..., - 32,-1, ,1,sqrt(2),2,Ď€ , ...} -3pt [0.6em]
As we can see, the whole numbers are part of the integers, the integers are a part of the rational numbers, and the rational numbers are a part of the real numbers. Another way to represent these sets is with a Venn diagram.
Rational numbers can be written as a fraction of two integers. A few examples are given below.
2/3, 2/1, 8/9
Notice that the middle number can be reduced to an integer. In fact, all integers can be written as a rational number by placing it in the numerator of a fraction with a denominator of 1. However, not all rational numbers, such as 23 and 89, can be written as integers. Therefore, the statement is sometimes true.
