Using number sets, it is found that the set of dense numbers is composed by: rational and irrational numbers
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Numbers can be classified as:
- Whole numbers: All positive numbers and 0, so: {0,1,2,...}
- Integer numbers: Positive or negative, not decimal so: {...,-2,-1,0,1,2,....}
- Rational numbers: Integer plus decimals that can be represented by fractions, that is, they either have a pattern, or have a finite number of decimal digits, for example, 0, 2, 0,45(finite number of decimal digits), 0.3333(3 repeating is the pattern), 0.32344594459(4459 repeating is the pattern).
- Irrational numbers: Decimal numbers that are not represented by patterns, that is, for example, 0.1033430290339, which can be approximated to the rational 0.1.
- Real numbers: Rational plus irrational.
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- A subset is dense of the rational numbers if all numbers can be approximated to rational numbers, and thus, rational and irrational numbers are dense.
A similar problem is given at https://brainly.com/question/10814303
