# On the lexicographic representation of numbers

@article{Manca2015OnTL, title={On the lexicographic representation of numbers}, author={V. Manca}, journal={arXiv: History and Overview}, year={2015} }

It is proven that, contrarily to the common belief, the notion of zero is not necessary for having positional representations of numbers. Namely, for any positive integer $k$, a positional representation with the symbols for $1, 2, \ldots, k$ is given that retains all the essential properties of the usual positional representation of base $k$ (over symbols for $0, 1, 2 \ldots, k-1$). Moreover, in this zero-free representation, a sequence of symbols identifies the number that corresponds to the… CONTINUE READING

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##### Publications referenced by this paper.

SHOWING 1-10 OF 12 REFERENCES

Zeroless Positional Number Representation and String Ordering

- Mathematics, Computer Science
- 2000

- 3
- Highly Influential

Gh . A Brief History of Zero

- 2008