We shall also refer to a point as backward nonsingular, with the obvious analogous meaning.
The notion of backward complete is defined analogously by exchanging the roles of $f$ and $f^{-1}$.
Extend this sequence of numbers backwards, defining $N_{-1}$, $N_{-2}$ and $N_{-3}$ by ......
Then $G$ is simply $g$ with its periodic string read backwards.
Let $A'$ be $A$ run backwards.
[In most adverbial uses, backward and backwards are interchangeable; as an adjective, the more standard form is backward: a backward shift.]
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