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Let $\{0, 1, 2, 3, 4, 5, 6, 7, 8, 9\}$ be the $10$ digits of the base $10$ system. The set of all finite sequences of those digits that don't start with a leading zero, together with the single one-element sequence $(0)$, can be bijectively mapped onto the natural numbers starting with 0, in the usual base $10$ way. Through this mapping, one can associate a function defined on one set with a function defined on another. For example, from the function of addition, $2+8 = 10$, so that means $(2) + (8) = (1, 0)$. The number of digits function is defined on the sequences, and it is simply the length of the sequence, and it can be associated, or "lifted", to the set of natural numbers themselves. So, does this mean the number of digits in $0$ is $1$, or $0$? I ask this question because I got contradictory answers in my previous question.

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marked as duplicate by user147263, daw, user91500, kjetil b halvorsen, Dario May 13 '15 at 12:05

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

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The number of digits in zero is $1$, since we have associated zero with the one-element sequence $(0)$, and the number of digits function is defined as the length of that sequence.

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