3.9.1: Expressing ability or possibility with "neng"
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能 (néng) is one of several Chinese words that is normally translated as "can" in English. However, 能 (néng) is used to emphasize one's ability or the possibility of something happening.
能 (néng) indicates ability when used with activities that are not consciously learned or studied.
The structure to use 能 (néng) to express "ability" is:
Subj. + 能 + Verb + Obj.
When used with activities that are consciously learned or studied, 能 (néng) generally means that circumstances do not allow execution of the action. In other words, it's not possible.
The structure to use 能 (néng) to express possibility is exactly the same:
Subj. + 能 + Verb + Obj.
From these examples we can see such circumstances might be pertaining to getting someone's consent or reliant on the speaker's health. If the speaker wishes to express that they are able to execute an action requiring a consciously studied skill, 会 (huì) can be used instead.
Because 能 (néng) can express possibility, it is often used to form polite questions, something like "would it be possible" in English: