Math Word Problem
posted by Anonymous .
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?

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
r=(q+5)/2
=(a/b+5)/2
=(a+10b)/2b
so that
q<r<5
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
Similar Questions

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 {} 
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} 
6TH GR. ALGEBRA
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 … 
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 
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? 
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. 
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? 
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. 
Math
The set of numbers which includes all positive numbers that are not decimals and which includes zero is the set of? 
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'?