hi!

what is the link between field, set and vector space?

ie

let V be a non empty set and K be a field and E be a subfield.

why isit that V is a vector space over K when a set is smaller than a field.

and when it comes to subfields and fields, K will be a vector space over E..

by saying that sth is a vector space over sth, does it just mean taht the 8 axioms of vector spaces are satisfied?

then what is the difference between vector space and field?

thanks!