Definition of dimension of a vector space (or subspace) being finite or infinite

Created almost 9 years ago, updated about 8 hours ago

A vector space is finite-dimensional if some finite list spans it; its basis then has a finite number of elements. Otherwise it is infinite-dimensional. Polynomials of degree at most $n$ form a finite-dimensional space; all polynomials form an infinite-dimensional space because arbitrarily high powers are independent.

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