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I have some candidates for the former case(x -> 0):

The variable approaches zero.
The variable approximates to zero.
The variable are closing zero.
The variable becomes more and more equal to zero.

I don't know which of those above are native expressions and if I can say:

The variable goes away from zero.

to convey the opposite meaning?

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    I'm not native English but I think that "are closing zero" is not gramtically correct nor idiomatic. And instead of "become more and more equal to zero", what about "the variable tends to zero"? – RubioRic Jul 12 '18 at 9:01
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    @RubioRic Seems great! Danke! – Lerner Zhang Jul 13 '18 at 3:34
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The variable approaches zero.

This is correct.

The variable approximates to zero.

This is grammatically correct, but actually means the variable is almost zero (for example 0.0001). It doesn't convey any movement of the variable.

The variable are closing zero.

This is incorrect, but "The variable closes towards zero" is fine for casual conversation. For a situation where perfect grammar is important though, this is not recommended.

The variable becomes more and more equal to zero.

I guess this is kind of okay. A lot of native speakers would definitely say this, but it's really incorrect because equal is binary. You can't really be a little bit equal (even though lots of people would still use it that way).

As for conveying the opposite meaning, there's actually not many options. "The variable goes away from zero." sounds a bit awkward, but I can't think of a better way to word it off the top of my head. Maybe someone else here can think of a good phrasing. Personally, I'd try a different approach altogether ("The variable's value increases").

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    The terms "converges" and "diverges" can be used as The variable diverges from zero. – James K Jul 12 '18 at 12:18
  • I think approximate as a transitive verb is alternative to converge here. – Lerner Zhang Jul 13 '18 at 6:28
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    @lerner I looked it up in some dictionaries, and while some do list approximate as a synonym of approach, it's always one of the last (and thus least appropriate) synonyms. Personally, as a native British English speaker, I would never take approximate to mean converge and don't recommend using it as such. Especially so in this context, where approximate's actual definition (to be close to) is potentially applicable. – Omegastick Jul 13 '18 at 6:37
  • @Omegastick Thanks for your reply. I saw this on Wikipedia: In other words, it is the amount of information lost when Q is used to approximate P. – Lerner Zhang Jul 13 '18 at 7:39
  • @lerner Yes, this means the amount of information that is lost when you substitute Q for P because Q is close to P. – Omegastick Jul 13 '18 at 7:49

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