You need to be careful about this ... I believe that in France (for example) zero is regarded as both positive and negative. So in France:
Non-negative integers: 1, 2, 3, 4, 5, ...
Positive integers: 0, 1, 2, 3, 4, 5, ...
Similarly, for some countries "Whole Numbers" is equivalent to all the integers, while in other countries it's the set { 0, 1, 2, 3, 4, ... } while in still other countries it's { 1, 2, 3, 4, ... }
There is no approach that uses "natural language" and is universal, and being aware of this is both frustrating and useful. Whether it is important is up to the individual.
It's hard to be more explicit that it is considered both.
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Added in edit
In speaking with a French colleague, he says that "inférieur" often means "less-than-or-equal-to" rather than "strictly-less-than", so the passage you quote would still imply that 0 is negative (and most likely also positive).
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Second edit:
> In France, "positive" means "supérieur à 0", and "supérieur à " means "greater than or equal to". Similarly, "négative" means "inférieur à 0", that is "less than or equal to 0".
> (We have the similar reaction towards the anglosaxon world and the introduction of nonnegative…)
Non-negative integers: 1, 2, 3, 4, 5, ...
Positive integers: 0, 1, 2, 3, 4, 5, ...
Similarly, for some countries "Whole Numbers" is equivalent to all the integers, while in other countries it's the set { 0, 1, 2, 3, 4, ... } while in still other countries it's { 1, 2, 3, 4, ... }
There is no approach that uses "natural language" and is universal, and being aware of this is both frustrating and useful. Whether it is important is up to the individual.