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I asked the following question on the English Usage page, and it made people furious why I didn't ask here. So I do: suppose $f(x,y)$ is a function of two variables and I want to say: "take the limit of $f$, as $x$ approches a given variable". Can I say "take the limit of $f$ on the first variable? Or take the limit over the first variable? Suppose from the context it is clear toward which variable $x$ is approaching.

kimchi lover
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M. Rahmat
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1 Answers1

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According to google's n-gram viewer, the best phrase is:

'take the limit of '

Do realise that the meaning is the same regardless, but you're better off saying what is most commonly used.

It actually doesn't really matter whether you refer to more than one variable or multiple. This is because it wouldn't make sense logically or semantically for it to change whether you are taking limits of multiple variables or just one; this is due to the fact that contextually the 'verb' is the same, just not the subject.

I can jump 'over' them. I can also jump 'over' him.

The object of the preposition does not affect it. However:

I rammed 'into' them.

I have had to change my preposition such that it matched the context of my verb.

The same applies here

yolo
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  • But "take the limit of $f$" means $\lim_{(x,y)\to(x',y')}f(x,y)$. What I mean here is $\lim_{x\to x'}f(x,y)$. – M. Rahmat Jan 06 '21 at 20:48
  • Doesn't really matter. the 'of', 'over', or 'on' should have no grammatical change. It wouldn't make sense logically or semantically for it to change whether you are taking limits of multiple variables or just one; this is due to the fact that contextually the 'verb' is the same, just not the subject. I'll explain further – yolo Jan 06 '21 at 20:51