Posted by **Anonymous** on Friday, October 9, 2009 at 8:10pm.

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 -
**MathMate**, Friday, October 9, 2009 at 8:47pm
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.

## Answer This Question

## Related Questions

- 6TH GR. ALGEBRA - EXTENDING THE LESSON If you add any two rational numbers, the...
- 9th grade - Name the set(s) of numbers to which 1.68 belongs. a. rational ...
- Math - Which statements is false? A. A decimal fraction has a multiple of 10 as ...
- Math - The set of numbers which includes all positive numbers that are not ...
- math - Tne union of the set of rational numbers and the set of irrational ...
- math - list all numbers from the given set {-9,-4/5,0,0.25,/3,9.2,/100} that are...
- math - There are 5 numbers in a set of data. There are no repeated numbers. ...
- Math - Need help on the question below. Which number belongs to the set of ...
- algebra - List all the numbers from the given set that are, a.natural numbers b....
- Algebra - 23. The ___ axis represents the independent variable. X? 21. Name the ...

More Related Questions