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Earn +20 ptsQ: What can irrational numbers be defined as?
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Why should a real number be rational or irrational?
Because irrational numbers are defined as real numbers which are not rational.
Why does a real number have to be rational or irrational?
Because irrational numbers are defined as all 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 are irrational numbers important?
pi and e are irrational numbers. Without them most of geometry, trigonometry, calculus or probability distributions would not be defined.
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.
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