Is Every Subset of a Finite Dimensional Space Also Finite Dimensional?

[Fringhe]

Homework Statement

How could I prove that the subset of a finite dimensional space is also finite dimensional?

Homework Equations

N/A

The Attempt at a Solution

I think it's more intuitive in the sense that since the vector space is finite dimensional the subset is forcibly finite dimensional.

 

[Fredrik]

What is the definition of "finite dimensional"?

Btw, I think you mean "subspace", not "subset".

 

[lanedance]

do you mean subspace?

any basis for the subpace will be contained in the finite dimensional space. What is the maximum number of linearly independent vectors in any subset of a finite dimensional space?