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I've seen a lot of contradictory information online when it comes to if $0 \in \mathbb{N}$ and I've been wanting to know if there's a definite answer to this or not. Any help is greatly appreciated.

Sumanta
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Aussie Mathematician
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    Different choices are made by different mathematicians or in different circumstances. Sometimes the context makes the choice clear; sometimes less so. And there are notations which are explicit – Henry Nov 15 '19 at 12:05
  • One thing is for sure: in every math book you encounter you should check what side the author has chosen. Also if you publish yourself then you must take a stand (without the obligation to defend that) and be clear about it. – drhab Nov 15 '19 at 12:06
  • Personally, though, I've never met anyone making the assertion that sum of natural numbers has no neutral element. –  Nov 15 '19 at 12:10
  • @Gae.S. Maybe the Romans did :-). – drhab Nov 15 '19 at 12:13
  • Some do, some don't. Most use positive integers for when they want to include and reserve natural numbers for indexing and such to avoid this I guess. – cemsicles Nov 15 '19 at 12:13
  • In Wikipedia, about Peano's axioms: The first axiom states that the constant 0 is a natural number:
    1. 0 is a natural number.
     – Bernard Nov 15 '19 at 12:17
  • @drhab I've never met a Roman. –  Nov 15 '19 at 13:18

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