Does "non-" prefixed to a two word phrase permit another hyphen before the second word? If I want to refer to an entity which is defined as the negation of another entity by attaching "non-" it se...
"Non-" is defined as "a prefix meaning 'not,' freely used as an English formative, usually with a simple negative force as implying mere negation or absence of something (rather than the opposite or reverse of it, as often expressed by un-).
At the linguistics conference, there were no / not / non- native speakers of Esperanto. They're all grammatically "valid", but they all mean different things - and pragmatically / idiomatically, only the no version is likely to be used.
Except "non" is not an English word, it is a prefix of Latin origin. Which is why American style manuals will always ask you to merge it with the subsequent word, without a hyphen. British rules differ, and the "non-" construction is frequently found in the literature. In any case, an isolated "non" is definitely wrong, in any flavo [u]r of the English language.
Non tutte le ciambelle riescono col buco (literally "Not all donuts come out with holes"). It usually gets a smile from another Italian speaker, because it's a nice way to conclude (even serious) discussions about things that are complex and not working 100% according to plan and for which there may be no solution. It's a wry verbal shrug.
You used the dash in the wrong place: what you have written is a (non-zero)–sum game, which makes no sense. When you start with a hyphenated word, like zero-sum, than to make another hyphenated compound, this time you use an en dash, making it a non–zero-sum game. I might be tempted to create an open compound, but non doesn’t stand alone.