- Thread starter
- #1

#### sbrajagopal2690

##### New member

- Jul 2, 2013

- 2

Consider the set of positive rational numbers Q+ . Consider the relation r defined by

(x,y) ∈ r<=> x/y ∈ Z. Show that r is a partial order and determine all numbers greater than 1/2.

- Thread starter sbrajagopal2690
- Start date

- Thread starter
- #1

- Jul 2, 2013

- 2

Consider the set of positive rational numbers Q+ . Consider the relation r defined by

(x,y) ∈ r<=> x/y ∈ Z. Show that r is a partial order and determine all numbers greater than 1/2.

You must show that this relation isConsider the set of positive rational numbers Q+ . Consider the relation r defined by (x,y) ∈ r<=> x/y ∈ Z. Show that r is a partial order and determine all numbers greater than 1/2.

a R a (reflexivity) for all;

if a R b and b R a then a = b (antisymmetry);

if a R b and R ≤ c then a R c (transitivity).

I have no idea what "determine all numbers greater than 1/2" could mean?

- Moderator
- #3

- Feb 7, 2012

- 2,765

Suppose that $p/q$ is greater than $1/2$ in this ordering (where $p/q$ is a fraction in its reduced form, so that $p$ and $q$ have no common factors other than $1$). Then $\left.\frac12\middle/\frac pq\right.$ is an integer. Simplify that compound fraction and see what that tells you about $p$ and $q$.... determine all numbers greater than 1/2.