Positive constant scalar definition

Question

In French when we say "$k$ est une constante positive", that means $k\geq 0$. But I remarked that using the same sentence in English, "$k$ is a positive constant", means that $k>0$. Can one explain to me why$ k$ is a positive constant scalar doesn't include $0$?

Answer 1

Because the working convention is that "positive" is not the same as "not negative".

(There are other discrepancies between countries about terminology, which later were spread through the rest of the world.)

Answer 2

This is just a matter of definition. I don't think that such conventions exist in general. Everyone uses a different definition, depending on his own preferences. So you should just take it as it is.

Answer 3

I'm surprised the terminology is different in French, but Wikipédia seems to agree:

Un nombre positif est un nombre qui est supérieur (au sens de : supérieur ou égal) à zéro [...] Zéro est un nombre réel positif [...] Lorsqu'un nombre est positif et non nul, il est dit strictement positif.

The most common usage in English is that zero is neither positive nor negative. That is "positive" is normally understood to be "strictly positive". In the same way, "greater than" is normally understood to mean "strictly greater than", as in $k>j$ (not $k\ge j$).