Science Fair Project Encyclopedia In mathematics, a monomial is
a particular kind of polynomial, having just one term. Given a
natural number n and a variable x, the power function defined by
the rule f(x)=xn is therefore a monomial. Given several unknown
variables (say, x, y, z) and corresponding natural number
exponents (say, a, b, c), the product of the resulting
univariate monomials is also a monomial (e.g., the function
determined by the rule f(x)=xaybzc). If coefficients are allowed
(this may not be consistent), then a constant multiple of a
monomial is also counted as a monomial (e.g., 7xaybzc). The most
obvious fact about monomials is that any polynomial is a linear
combination of them, so they can serve as basis vectors in a
vector space of polynomials - a fact of constant implicit use in
mathematics. An interesting fact from functional analysis is
that the full set of monomials tn is not required to span a
linear subspace of C[0,1] that is dense for the uniform norm
(sharpening the Stone-Weierstrass