"A subspace is any subset of a vector space."

[Seimuna]

"A subspace is any subset of a vector space."
Why is this statement wrong?

As i know, subspace is a subset of a vector space that is closed under addition and scalar multiplication, right? The how come is wrong?

 

[TheOli]

because not all subsets are closed under addition ext

 

[nezenic]

I tend to think of it this way:

A subspace is a vector space of a vector space.

Not just any subset of a vector space.