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According to a dictionary, 'week' is a countable noun. e.g. a whole week. But, in the following phrases "last/next/all week", any determiner can't be seen. In what ways should I interpret that? I should think all week should be all weeks.

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anonymousI should think all week should be all weeks.

No, all week and all weeks have different meanings.

All week would mean "Through the whole week", or "on every day of the week".

"She was sick all week and didn't come to work at all".

All weeks would be another way of saying every week, but would only be a suitable replacement for every week in certain circumstances, for example when discussing the results of a study to see how often certain events occurred over a period of time that was divided into weeks.

"Mistakes were found in the weekly totals in all weeks, but in only two cases did the amount involved exceed $10"