- #1
tomboi03
- 77
- 0
Show that the countable collection
{(a,b) x (c,d) | a<b and c<d and a,b,c,d are rational}
is a basis for R2.
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 B1 and B2, then there is a basis element B3 containing x such that B3[tex]\subset[/tex]B1[tex]\cap[/tex]B2.
right? or am i wrong?
Thank You,
Jonnah Song
{(a,b) x (c,d) | a<b and c<d and a,b,c,d are rational}
is a basis for R2.
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 B1 and B2, then there is a basis element B3 containing x such that B3[tex]\subset[/tex]B1[tex]\cap[/tex]B2.
right? or am i wrong?
Thank You,
Jonnah Song