TITLE: If the digit sum function would be valid for base 1, would it mean that the digit sum of n in base 1 be equal n?
QUESTION [0 upvotes]: Let us define $n \in \mathbb{N} \setminus \{0\}$ and let us define the digit sum function for the base $b$ as $F_b(n)$ (according to wikipedia).
Also as mentioned in the previous wikipedia link the base is $b \ge 2$.
What I am asking myself is if $b$ could be $1$, would this mean that $F_1(n) = n$?
If this should be true then we could say that the basic counting is similar (or equal?) to counting of $1$'s for the number $n$ in base $1$?

REPLY [2 votes]: Base $n$ has digits $0, 1, ..., n-1$
Base 1 would only have $0$ as a digit, so is impossible to use as a way to represent numbers.
Therefore $b\ge2$
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