True/False Question :
There exists an injective ring homomorphism from the product ring $\mathbb{R}\times \mathbb{R}$ into $C\left ( \mathbb{R} \right )$, where $C\left ( \mathbb{R} \right )$ denotes the ring of all continuous functions $\mathbb{R}\rightarrow \mathbb{R}$ under pointwise addition and multiplication.