I notice these two words come out frequently, but the meaning seems like be different. Who can tell me what is the difference.
If possible give me some examples too.
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己, as a single character, means "self". Since 自 has the same meaning. the 自己, as a noun in a sentence, means "self".
已 as a single character has multiple meanings, which I won't explain much here. 自已, as a verb, is only used in genitive sentences and means (cannot) control my (or her or his) motion. For example:
We can say: 我愤怒地不能自已。 他激动地难以自已。 她悲伤地无法自已
We don't say: 他自己了激动的心情。
An ultimate example: 我听到自己被耶鲁大学录取的消息时，激动地无法自已。
Remember, 自已 is only used in negative sentences and only means (cannot) control the motion. This is because of the 词语的固定搭配 and 用语习惯.