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The phrase 何况 (hé kuàng) is a conjunction used in Chinese to indicate that what follows is an even stronger or more obvious point than what has just been stated. It can be translated as "let alone," "not to mention," or "much less" in English. This structure is often used to emphasize a contrast or to highlight an additional point that reinforces the argument being made.
In the examples provided:
我不道歉，何况根本不是我的错！
Translation: "I won't apologize, let alone it's not my fault at all!"
Here, the speaker emphasizes that not only will they not apologize, but it is also unnecessary because they believe they are not at fault.
这道菜做起来很花时间的，何况今天顾客那么多。
Translation: "This dish takes a lot of time to prepare, not to mention there are so many customers today."
In this case, the speaker highlights that the time-consuming nature of the dish is compounded by the fact that there are many customers, making the situation even more challenging.
In summary, 何况 is used to introduce a point that adds weight to the previous statement, often indicating that the subsequent information is even more significant or relevant. It is a useful structure for making arguments more persuasive and for emphasizing contrasts in various contexts.