The real number system includes all numbers we can place on a number line. Natural numbers, whole numbers, integers, rational numbers, and irrational
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Is zero a natural number?
This depends on the definition. In some definitions, natural numbers start from 1. In other definitions, particularly in set theory and logic, natural numbers include 0. Both conventions are used in mathematics. Whole numbers always include 0 in addition to natural numbers.
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Are all decimals irrational?
No, only non-repeating, non-terminating decimals are irrational. Decimals that terminate like 0.25 are rational. Decimals that repeat like 0.333... are rational. Only decimals that never repeat and never terminate like pi are irrational.
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How many irrational numbers are there?
There are infinitely many irrational numbers, actually more than rational numbers. While both sets are infinite, mathematicians have proven that irrational numbers are more numerous than rational numbers. This is a surprising and non-intuitive result.
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