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I used to write and review problems for math competitions. This is why we avoided saying "natural numbers". We used "nonnegative integers" or "positive integers

by qsort 1y ago

I used to write and review problems for math competitions. This is why we avoided saying "natural numbers". We used "nonnegative integers" or "positive integers" instead.

ColinWright 1y ago
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.
- thaumasiotes 1y ago
  > I believe that in France (for example) zero is regarded as both positive and negative. That would cause all kinds of problems, so I'd be pretty surprised if it turned out to be true. I note that this is the heading of the relevant wikipedia page: > Un nombre négatif est un nombre réel qui est inférieur à zéro, comme −3 ou −π. ( https://fr.wikipedia.org/wiki/Nombre_n%C3%A9gatif https://fr.wikipedia.org/wiki/Nombre_n%C3%A9gatif ) It'd be hard to be more explicit that zéro is not a negative number.
  - ColinWright 1y ago
    If you're going to quote wikipedia: > "Zéro est le seul nombre qui est à la fois réel, positif, négatif et imaginaire pur." From: https://fr.wikipedia.org/wiki/Z%C3%A9ro#Propri.C3.A9t.C3.A9s_arithm.C3.A9tiques_et_alg.C3.A9briques https://fr.wikipedia.org/wiki/Z%C3%A9ro#Propri.C3.A9t.C3.A9s... It's hard to be more explicit that it is considered both. ================ 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). ================ 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…) -- https://mathstodon.xyz/@antoinechambertloir/115327589116457527 https://mathstodon.xyz/@antoinechambertloir/1153275891164575...
- dooglius 1y ago
  Presumably, GP only worked on the problems in English and someone else would translate it appropriately.

by qsort 1y ago

I used to write and review problems for math competitions. This is why we avoided saying "natural numbers". We used "nonnegative integers" or "positive integers" instead.

ColinWright 1y ago

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.

thaumasiotes 1y ago
> I believe that in France (for example) zero is regarded as both positive and negative. That would cause all kinds of problems, so I'd be pretty surprised if it turned out to be true. I note that this is the heading of the relevant wikipedia page: > Un nombre négatif est un nombre réel qui est inférieur à zéro, comme −3 ou −π. ( https://fr.wikipedia.org/wiki/Nombre_n%C3%A9gatif https://fr.wikipedia.org/wiki/Nombre_n%C3%A9gatif ) It'd be hard to be more explicit that zéro is not a negative number.
- ColinWright 1y ago
  If you're going to quote wikipedia: > "Zéro est le seul nombre qui est à la fois réel, positif, négatif et imaginaire pur." From: https://fr.wikipedia.org/wiki/Z%C3%A9ro#Propri.C3.A9t.C3.A9s_arithm.C3.A9tiques_et_alg.C3.A9briques https://fr.wikipedia.org/wiki/Z%C3%A9ro#Propri.C3.A9t.C3.A9s... It's hard to be more explicit that it is considered both. ================ 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). ================ 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…) -- https://mathstodon.xyz/@antoinechambertloir/115327589116457527 https://mathstodon.xyz/@antoinechambertloir/1153275891164575...
dooglius 1y ago
Presumably, GP only worked on the problems in English and someone else would translate it appropriately.