Bijective Numeration

Bijective numeration is any numeral system that establishes a bijection between the set of non-negative integers and the set of finite strings over a finite set of digits. In particular, bijective base-k numeration represents a non-negative integer by using a string of digits from the set {1, 2, ..., k} (k ≥ 1) to encode the integer's expansion in powers of k. (Although slightly misleading, this is the terminology in the literature. Ordinary base-k numeration also establishes a bijection, but not in the required sense, due to the absence of leading zeros; for example, there are only 90 two-digit decimal numerals, rather than the required 102.) Bijective base-k numeration is also called k-adic notation, not to be confused with the p-adic number system. Bijective base-1 is also called unary.