Real numbers encompass any number along the number line, infinitely. Integers, whole numbers, natural numbers, etc. are are real numbers.
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Because irrational numbers are defined as all real numbers which are not rational.
Because irrational numbers are defined as real numbers which are not rational.
Yes.
The set of real numbers is defined as the union of all rational and irrational numbers. Thus, the irrational numbers are a subset of the real numbers. Therefore, BY DEFINITION, every irrational number is a real number.
The different names for Numbers are defined as Natural numbers, whole numbers , real numbers, decimal numbers, integers, rational numbers and irrational numbers.