Monomials of Polynomial Ring are Linearly Independent/One Variable

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

Let $R[X]$ be a polynomial ring in one variable $X$ over $R$.

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

Also see

 * Equality of Monomials of Polynomial Ring in One Variable