Talk:Q28920044

Redundant?

Hi Infovarius! Considering that

⟨ positive integer (Q28920044)    ⟩ subclass of (P279) ⟨ non-negative integer (Q28920052)    ⟩

and

⟨ non-negative integer (Q28920052)    ⟩ subclass of (P279) ⟨ natural number (Q21199)    ⟩

it follows by transitivity of subclass of (P279) that

⟨ positive integer (Q28920044)    ⟩ subclass of (P279) ⟨ natural number (Q21199)    ⟩

So, do we need to specify that explicitly? Helder 10:04, 9 February 2018 (UTC)

Good point. But I suspect that

⟨ non-negative integer (Q28920052)    ⟩ subclass of (P279) ⟨ natural number (Q21199)    ⟩

is not correct for all definitions of natural number (Q21199)... --Infovarius (talk) 11:10, 11 February 2018 (UTC)

The existence of the item natural number (Q21199) makes things really confusing. There are only two relevant concepts here:

1. The set $\{x\in \mathbb {Z} \mid x>0\}$ (positive integer (Q28920044))
2. The set $\{x\in \mathbb {Z} \mid x\geq 0\}$ (non-negative integer (Q28920052))

It is ok to call either of them the set of "natural numbers" and to represent either by $\mathbb {N}$. But I don't see much point in having also natural number (Q21199) (is it about the English expression "natural number" which could mean any of the concepts above? Wouldn't that be simply a disambiguation?), so I'm not sure it deserves any (mathematical) properties (e.g. "disjoint union of 1, prime number and composite number" - which applies to the meaning positive integer (Q28920044) not to non-negative integer (Q28920052)). Helder 16:14, 11 February 2018 (UTC)

I understand that it is ambiguous (in Russian too). But most of the times it means first choice (we were taught that only formal Bourbakists consider the second variant) and it has good genuine definition itself, so I also understand why the item natural number (Q21199) exists. --Infovarius (talk) 00:20, 15 February 2018 (UTC)