Math Word Problem

posted by .

Let A be the set containing all rational numbers that are less than 5. Is there a rational number q in set A such that all other numbers in set A are less than q? Why or why not?

  • Math Word Problem -

    We will try to prove this by contradiction.

    Hypothesis: existence of q=a/b which is the largest rational number less than 5, i.e. q=a/b<5 and b≠0, and that no other rational number exists that is larger than q and less than 5.

    We will calculate the r, the average between q and 5
    so that
    which means that
    r is greater than q,
    r is less than 5, and
    r is rational.

    Therefore that hypothesis that q exists is false.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. math

    Tne union of the set of rational numbers and the set of irrational numbers is 1 {whole number} 2 {real numbers} 3 {counting numbers} 4 {}
  2. algebra

    List all the numbers from the given set that are, a.natural numbers b.whole numbers c.integers d.rational numbers, e.irrational numbers {-9,-4/5,0,0.25,ã3,9.2,ã100}

    EXTENDING THE LESSON If you add any two rational numbers, the sum is always a rational number. So, the set of rational numbers is closed under addition. Is the set of rational numbers closed under subtraction. multiplication,and division …
  4. 9th grade

    Name the set(s) of numbers to which 1.68 belongs. a. rational numbers b. natural numbers, whole numbers, integers, rational numbers c. rational numbers, irrational numbers d. none of the above my answer a)rational numbers
  5. Math

    Need help on the question below. Which number belongs to the set of rational numbers but does not belong to the set of whole numbers?
  6. math

    list all numbers from the given set {-9,-4/5,0,0.25,/3,9.2,/100} that are a) whole numbers b) natural numbers c) intergers d) rational numbers e) irrational numbers.
  7. math

    There are 5 numbers in a set of data. There are no repeated numbers. Which measure of data must represent a number in the set that is greater than 2 of the numbers in the set and less than 2 of the numbers?
  8. Math

    Which statements is false? A. A decimal fraction has a multiple of 10 as a denominator. B. Every rational number can be associated with a point in the real number line. C. A terminating decimal cannot be expressed as a repeating decimal.
  9. Math

    The set of numbers which includes all positive numbers that are not decimals and which includes zero is the set of?
  10. Algebra

    Please Help!!!! thanks :) 1. Suppose U= {1,2,3,4,5,6,7,8,9,10} is the universal set, and P= {2,4,6,8,10}. What is P'?

More Similar Questions