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Earn +20 ptsQ: How is a real number defined?
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Why does a real number have to be rational or irrational?
Because irrational numbers are defined as all real numbers which are not rational.
Why should a real number be rational or irrational?
Because irrational numbers are defined as real numbers which are not rational.
Is every irrational number a real number and how?
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.
Why does any real number must be either a rational number or an irrational number?
It is due to the fact that the set of real numbers is defined as the union of the rational and irrational numbers.
Can have two real numbers if the quotient is not real number?
Yes but only if the denominator is 0 (so the quotient is not defined).
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