Simulations between Turing machines
As I understand your question, the double-sided machine has a tape indexed by $\mathbb{Z}$ and the one-sided has a tape indexed by $\mathbb{N}$.

The question then boils down to finding a bijection f between the two sets st. $\forall z \in \mathbb{Z}: |f(z) - f(z+1)| &lt; k$ for some constant k. Can you find such a bijection:

Hint: k = 3 is sufficient.