- #1
kent davidge
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Does it make sense to say that a set together with a field generates a vector space? I came across this question after starting the thread https://www.physicsforums.com/threads/determine-vector-subspace.941424/
To be more specific, suppose we have a set consisting of two elements ##A = \{x^2, x \}## and let the reals ##\mathbb{R}## be the field. The set ##A## doesn't form a vector space, but it generates a vector space, the space of all polynomials of the form ##ax^2 + bx##, which by the way is a subspace of ##P^2(x)## which is discussed on that thread.
Is my thought about generating instead of forming correct?
To be more specific, suppose we have a set consisting of two elements ##A = \{x^2, x \}## and let the reals ##\mathbb{R}## be the field. The set ##A## doesn't form a vector space, but it generates a vector space, the space of all polynomials of the form ##ax^2 + bx##, which by the way is a subspace of ##P^2(x)## which is discussed on that thread.
Is my thought about generating instead of forming correct?