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n. middle, center; inside
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In this note, we will compare 中 and 里, two nouns of locality.

1. Sometimes 里 and 中 are interchangeable. This is when they both refer to a place, a period of time or the inside of something.
Examples: 心里/心中 (in one's mind, in one's heart), 眼里/眼中 (in one's eyes), 村子里/村子中 (in the village)

2.When referring to a process, a status or something abstract, something that is infinitely large, 中 is used. 里 is incorrect in these contexts.
这个案子目前还在调查中。This case is still under investigation.
他在交谈中流露出一丝不耐烦。During the conversation, he showed a little impatience.

3. When referring to a social unit, person in charge or the members of the social unit, only 里 is used.
Example: 去年厂里决定购买一批新设备。Last year, the factory decided to purchase a new batch of equipment.
Here 厂里 does not literally mean to "the inside of a factory", instead, it refers to the factory itself as a social unit, or to be more specific, "the person/people who is/are in charge of purchasing the new equipment".
里 vs 内 vs 中:

里, 内 and 中 are all nouns of locality (=nouns that show direction and location). Whare are their differences?

1. 里 and 内 can be independently used as a noun or as a noun immediately preceded by a preposition; 中 cannot be used in these two ways.

1a. When 里 and 内 are used independently as a noun, they are limited to a few idioms or fixed phrases; 内 usually appears in written Chinese. In these examples below, 里 and 内 are NOT interchangeable, because they are idioms or fixed phrases:
里应外合 lǐ yìng wài hé [idiom] to collaborate from within with forces from outside
由表及里 yóu biǎo jí lǐ [idiom] from the outside to the inside, from the surface to the centre
请勿入内 qǐng wù rù nèi ! [phr] No entry!

1b. When following a preposition, 里 is limited to these prepositions -- 往, 朝, 从, 由, 向, while 内 is used with 由, 在, 从. For example:
Prep. 里: 往里走, 朝里看, 从里到外, 由里往外
Prep. 内: 由内而外, 计算在内, 从内到外

2. 里, 内 and 中 can all be used after a noun. In other words, they can all appear in the structure "Noun ___", indicating location, time or range, etc.. But there are some differences.

2a. 内 and 中 are used in written Chinese (more formal), while 里 is used in spoken Chinese (more informal and casual). For example:
家里 vs 家中
房间里 vs 房间内,房间中

2b. When 内 appears in "Noun ___" and indicates location or range, the preceding noun is usually (but not always) mono-syllabic. For example:
Indicating location: 校内, 室内, 场内, 市内
Indicating range: 党内, 学术团体内

2c. 中 can be used to indicate a state or a situation, and in this case it usually appears after prep such as 在 or 从. Note that 内 and 里 cannot be used in this way:
e.g. 在欢乐的气氛中 (in a happy atmosphere), 从昏迷中苏醒过来 (to come out of a coma)

2d. 里 can be used with a preceding noun that is an organization or agency, referring to the organization itself or the place where it’s located. e.g. 县里, 厂里, 机关里, 家里

2e. 里 and 中 can be used with a preceding noun that is a human body part it can carry on a figurative meaning. The difference is that 里 is informal and 中 is formal. e.g. 手里/手中, 嘴里/嘴中, 心里/心中. 内 cannnot be used in this way. For example,
手里(or 手中)掌握了一些信息 (figurative meaning: get hold of some information; not actually holding a tangible object in one's hand)

3. 里, 内 and 中 can all be used before a noun. In other words, they can all appear in the structure "___ Noun", acting as some sort of modifier to the noun. But there are some differences and Chinese learners might need to memorize the combinations one by one.

3a. 中 indicates a place between two extremes, somewhere in the middle. For example:
- Indicating the position. e.g. 中途, 中指, 长江中游
- Indicating the time. e.g. 中秋, 中古时期
- Indicating the level or scale. e.g. 中篇小说, 中学, 中型, 中号

3b. 里 is usually used before a monosyllabic noun. 内 acts as a modifier to the noun, but it's reduced to a morpheme and its function is to construct words. For example:
内室, 内河
里屋, 里院
Sometimes, 里 and 内 are interchangeable, for example we can also say 内屋 and 内院.

4. Among the three, only 中 can appear after a verb. In other words, only 中 can appear in the structure "Verb ___", indicating the process or a continuous state. For example:
- Indicating the process: 讨论中 (when discussing), 会谈中 (during the meeting)
- Indicating a continuous state: 在写作中 (while writing)

5. Among the three, only 内 can appear before a verb. In other words, only 内 can appear in the structure "___ Verb". In this case, 内 acts as a modifier but it's reduced to a morpheme and its function is to construct words. For example:
内分泌 nèi fēn mì [n] endocrine (internal secretion, e.g. hormone)
内出血 nèi chū xiě [phr] internal bleeding

6. Among the three, only 里 can appear after an adjective. In other words, only 内 can appear in the structure "Adjective ___", indicating direction or aspect. The adjectives are usually mono-syllabic. For example:
往好里想 wǎng háo lí xiǎng [phr] to think in a more positive way
横里看,竖里看 héng lǐ kàn , shù lǐ kàn [idiom] to look at something from all different angles or perspectives
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