My attempt to solve this:
If $\mathcal{A}$ is an arbitrary infinite recursive set then the members of $\mathcal{A}$ can be ordered in ascending order. We can do bijection between $\mathcal{N}$ and $\mathcal{A}$.
Halting problem is $\mathcal{K}\subseteq\mathcal{N}$ and therefore it's also $\mathcal{K}\subseteq\mathcal{A}$. And the same can be said about $\bar{\mathcal{K}}$.
Is my solution correct? Are there any "better" solutions to this problem?
