Identity function that returns $1$ for the input $0$. I'm looking for a way to write the following function:
\begin{equation}
id(x) = \begin{cases}
x & x \neq 0 \\
1 & x = 0
\end{cases}
\end{equation}
However, I want to implement it without using conditionals. Any ideas? The simpler, the better.

As @JohnHughes points out, normal algebra can't help you. If you're willing to use the Kronecker delta function  then
$$
f(x) = x + \delta(x,0)
$$
does what you want.
