Sorry Tim, I am regret to tell you what you said is not totally correct. As a Chinese, I probabily know what you mean. In KangXi Dictionary of Qing dynasty, there are 47035 Chinese characters. And that doesn't include all the characters inside although it's the most representitive Chinese character dictionary. And combination of characters form some meaningful unit [we call them 'Chinese phrase'. e.g., English word, 'study', in Mandarin Chinese will be printed as 'du shu(in Pinyin)' or '??(in Chinese characters)' that include 2 Chinese characters] that could be translated into English as words, or phrases. 6000 Chinese phrases will be sufficient for almost every situation in everyday communication or even in communicate in written form. However, 6000 Chinese phrases will include far more than 6000 Chinese characters.
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