Is Zero a Natural Number?

TL;DR

This paper discusses the conceptual distinction between zero as a cardinal number and as an ordinal number, emphasizing the importance of differentiating order types from ordinal labels.

Contribution

It clarifies the conceptual distinction between zero's roles as a cardinal and an ordinal, proposing a clearer understanding of their differences.

Findings

Zero should be considered a cardinal number

Zero should not be considered an ordinal number

Distinction between order types and ordinal labels is crucial

Abstract

It is argued that zero should be considered as a cardinal number but not an ordinal number. One should make a clear distinction between order types that are labels for well-ordered sets and ordinal numbers that are labels for the elements in these sets.