Monomials of Polynomial Ring are Linearly Independent/One Variable

Theorem
Let $R$ be a commutative ring with unity.

Let $R \sqbrk X$ be a polynomial ring in one variable $X$ over $R$.

Then the set of monomials $\set {X^k : k \in \N}$ is linearly independent.

Also see

 * Equality of Monomials of Polynomial Ring in One Variable