So I've been given rings $R = Map(\mathbb{R},\mathbb{R})$ and $S = (a_{n})_{n \geq 0}$ such that $a_{n} \in \mathbb{R}$ and the ring homomorphism
$$ \phi: R \rightarrow S\\ f \rightarrow (f(n))_{n} $$
And an ideal for the ring homomorphism $I = \{f \in R | f(n) = 0 \text{ for all } n \in \mathbb{N}\}$ and a constant function $\mathbf{1}: x \mapsto 1$
I need to find a non-constant function $f$ such that $f + I = \mathbf{1} + I$. I understand that this means that I need to find a function such that $f - \mathbf{1} \in I$. And that in simpler terms that it means I need a non-constant function $f$ such that $f(n) - 1 = 0 \text{ for all } n \in \mathbb{N}$ but I can't think of any such function that isn't constant.