Integers are whole numbers. Fractions, whether in decimal or divisional form, can be either rational or irrational.
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There are no integers which are irrational.
An integer has to be a whole number or its opposite. For example, fractions and decimals cannot be integers. I'm smart (:
Integers are whole numbers without fractions or decimals
Non-integers are fractions, decimal numbers, and irrational numbers. Integers are positive and negative whole numbers.
Whole numbers without decimals or fractions are called integers.