Real numbers $x$ satisfying $x \geq 0$ are said to be non-negative. Some alternative phrases include positive or zero and at least zero. However, I find these phrases to be unsatisfactory, for a couple of reasons.
One. With the exception of non-negative, these phrases are a bit long-winded, and they don't function like adjectives, which is also annoying. For example, the sentence "the natural numbers are the positive or zero integers," doesn't sound particularly grammatical.
Two. The logical negation in the phrase "non-negative" is slightly confusing. I think it probably confuses new students, since I've been studying mathematics for a long time and still sometimes feel a moment of confusion when I hear this phrase.
Three. It's a fundamental concept that's introduced early on in people's mathematical careers and relates to lots of basic stuff people need to master. It's involved in the very important law $$a \geq 0 \rightarrow (x \leq y \rightarrow ax \leq ay),$$ its the domain on which $\sqrt{x^2} = x$, and its the codomain of every norm and metric. It also describes the length/area/volume of compact shapes, which are pretty much the only shapes people look at in high school. Hence having a short and spiffy term for it would be pedagogically useful.
Four. Mathematically speaking, it doesn't generalize well. In a partially-ordered field or partially-ordered ring, non-negative ought to mean $\neg(x < 0)$, which is a weaker condition than $x \geq 0$.
Question.
When I was younger, I came up with the word "positic" to describe numbers $x$ satisfying $x \geq 0$. My friends toyed with it for awhile, but we ultimately found it was a bit cringeworthy phonetically, and eventually we stopped using it. I'd be interested to know if there's anywhere in the world where there's a word for this concept, or if any words have been proposed. In short: is there a better term for "non-negative"?