[gizmo686]

>A working definition of a space might be - you have a member in that space, you can get to every other member by just scalar mult.

Isn't this a 1 dimensional space. Eg. Consider the vector space R2 over R.

If you have the vector (1,0), there is no way to arrive at the vector (1,1) through just scalar multiplication.

[dxbydt]

if you don’t give me basis how’ll i span the space ?

[zazen]

You talked about having "a member" and getting to every other member with scalar multiplication only. But even given a 2-member basis for R2, how are you planning on using 2 members, with scalar multiplication only?

I'm afraid you have badly misremembered this stuff.

[dxbydt]

you are right.