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"An invention should be described in its dynamic state. The dynamic state is understood as a state in which... " "An invention should be described in its dynamic state. A dynamic state is understood as the state in which... " In this case, the articles can be used interchangeably.


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In your example, the reader understands when the wickets occur, both a loss of 8 wickets and the loss of 8 wickets are acceptable. Usually, the latter is used in commentary.


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Your statement sounds rude and confronting to be honest. You could think of pursuing a more considerate approach as follows: My apologies, but this doesn't look like a syllabus. This is more like your teaching methods in the class. Do you mind sending the correct document again? However, if you are willing to stick to your approach, I must say, there is no ...


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"In such case" and "in such a case" are both possible. I compared their frequencies at Google Ngram Viewer, which showed that both phrases have very similar frequencies. I also included "in such cases", and found that it is more common than either of the other two: Google Ngram Viewer This dictionary shows "such" as ...


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It depends on which sense of "proof" you want. Going down Merriam-Webster's list 1a: the cogency of evidence that compels acceptance by the mind of a truth or a fact 3: something that induces certainty or establishes validity 5: evidence operating to determine the finding or judgment of a tribunal These meanings are usually used uncountably, with ...


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