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Relations and Functions

sbrajagopal2690

New member
Jul 2, 2013
2
need help on this ..any suggestions are highly appreciated


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.
 

Plato

Well-known member
MHB Math Helper
Jan 27, 2012
196
Re: relations and functions

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 is
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?
 

Opalg

MHB Oldtimer
Staff member
Feb 7, 2012
2,708
... determine all numbers greater than 1/2.
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 $q$.