{(a,b) x (c,d) | a<b and c<d and a,b,c,d are rational}

is a basis for R

^{2}.

I was wondering... if i have to use the definition of a basis in order to solve this?

soo... meaning.. a basis:

Axioms:

1. for each x [tex]\in[/tex]X, there is at least one basis element B containing x.

2. If x belongs to the intersection of two basis elements B

_{1}and B

_{2}, then there is a basis element B

_{3}containing x such that B

_{3}[tex]\subset[/tex]B

_{1}[tex]\cap[/tex]B

_{2}.

right? or am i wrong?

Thank You,

Jonnah Song