Translation suggestion of an operation - adding and subtracting the same term - German: Nullergänzung How would one call this operation in English where we add a term $a$ and subtract the additive inverse $-a$ right away again, so $$ f(x)-g(x)=f(x)-a+a-g(x) $$ for example here where we also use the triangle inequality $$ |x|= |(x + y)−y|\leq|x+y|+|y|\iff |x| − |y| \leq |x + y| $$ where we added and subtracted $y$. I just couldn't find a proper translation, in German one would call it for example **_nahrhafte Null_** or **_Nullergänzung_** which literally means _nutritious zero_ and _zero completion/addition_ respectively, though I have never read those translations anywhere, ever. Other languages might also be interesting but I am mostly interested in English. Are there any dictionaries out there which mainly focus on mathematical terminology?

I had a great teacher in high school, named John Titterton. He called this a "propitious zero." When multiplying and dividing by the same thing, he called it a "propitious one." My guess is that he invented these phrases himself. They work well.

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