How does the definition of natural numbers differ from the definition of integers?
Always
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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 Natural& [-0.5em] Numbers & & -3pt {1,2, ... } -3pt [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, ,2,sqrt(2),2,Ď€ , ...} -3pt [0.6em]
As we can see, the natural numbers are a part of the whole numbers, the whole numbers are a part of the integers, and so on. Another way to represent these sets is with a Venn diagram.
As we can see, natural numbers are a subset of integers. Therefore, a natural number is always an integer.
