Question 6
Sum and invert - using only the two operations "+1=\text{add 1}" and "$-i=\text{minus the reverse}$", we can form several sequences from an initial number. For example, starting with the number $3$, we can form the sequence $$
3 \xrightarrow{+1} 4 \xrightarrow{+1} 5 \xrightarrow{-i}-\frac{1}{5} \xrightarrow{+1} \frac{4}{5} \xrightarrow{-i}-\frac{5}{4} \xrightarrow{+1}-\frac{1}{4} \xrightarrow{+1} \frac{3}{4} \xrightarrow{-i}-\frac{4}{3} .
$$ starting with $0$, with which sequence we will retrieve the $0$, using only these two operations "+1" and "$-i$"?
3 \xrightarrow{+1} 4 \xrightarrow{+1} 5 \xrightarrow{-i}-\frac{1}{5} \xrightarrow{+1} \frac{4}{5} \xrightarrow{-i}-\frac{5}{4} \xrightarrow{+1}-\frac{1}{4} \xrightarrow{+1} \frac{3}{4} \xrightarrow{-i}-\frac{4}{3} .
$$ starting with $0$, with which sequence we will retrieve the $0$, using only these two operations "+1" and "$-i$"?