SOLUTION: How many points, integers, rational and irrational numbers are in each of these sets? What lengths are associated with each of the sets? 1) {3} 2) {3, 4} 3) [2, 4) 4) [3, 8]

Algebra ->  Real-numbers -> SOLUTION: How many points, integers, rational and irrational numbers are in each of these sets? What lengths are associated with each of the sets? 1) {3} 2) {3, 4} 3) [2, 4) 4) [3, 8]      Log On


   

Question 178505: How many points, integers, rational and irrational numbers are in each of these sets? What lengths are associated with each of the sets?
1) {3}
2) {3, 4}
3) [2, 4)
4) [3, 8]
Answer by solver91311(24713) About Me  (Show Source):
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There is a point on the number line associated with each element of any enumerated set where the elements are numbers.

Integers are the positive and negative whole numbers. Rational numbers are all of the numbers that can be represented as the ratio of two integers. Remember all integers are rational because you can represent any integer as that integer divided by 1 which is itself an integer. An irrational number is any real number that is not rational, that is it cannot be represented as the ratio of two integers.

In any interval, there are an infinite number of points between the end points, regardless of whether the end points are included or not.

Between any two rational numbers, there are an infinite number of real numbers, including an infinite number of rational numbers and an infinite number of irrational numbers. Same thing holds for any pair of irrational numbers.