Tuesday

October 21, 2014

October 21, 2014

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

- Math Word Problem -
**MathMate**, Friday, October 9, 2009 at 8:47pmWe 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 - What is the best sequence of names to identify this set of numbers? (1 3/...

math- please help - What is the best sequence of names to identify this set of ...

Math - Identify all sets to which the number 3 belongs A. Whole numbers, ...

Maths - Find the denominator n of the rational number kn (k,n are both integers...

Math - Which statement is correct? A. All intergers are rational numbers. B. All...

math - 1. Which of the following numbers is an example of an integer? a. -15 b. ...

math - Tne union of the set of rational numbers and the set of irrational ...

Algebra - 23. The ___ axis represents the independent variable. X? 21. Name the ...