Decimal sequence/Primary school/Mapping/Properties/Exercise

We consider the mapping

$f\colon \mathbb {N} \longrightarrow \mathbb {N}$

that is described in exercise (the natural numbers are given as finite sequences in the decimal system).

1. Is ${}f$ increasing?
2. Is ${}f$ surjective?
3. Is ${}f$ injective?
4. Does ${}f$ have a fixed point?

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