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.
Irrational numbers are the real numbers that cannot be expressed as the ratio between two integers. A few examples are given below.
sqrt(2), π and sqrt(5)
These numbers, however, are real numbers, because they can be placed on a number line. Therefore, the statement that an irrational number is a real number is always true.
