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A week starts with Monday (day 1) and ends with Sunday (day 7).
For example, the first week of the year 1997 lasts from 1996-12-30 to 1997-01-05 and can be written in standard notation as for applications like industrial planning where many things like shift rotations are organized per week and knowing the week number and the day of the week is more handy than knowing the day of the month.
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Apart from the recommended primary standard notation YYYY-MM-DD, ISO 8601 also specifies a number of alternative formats for use in applications with special requirements.
Possible ISO week numbers are in the range 01 to 53. (There is one historic exception: the year in which the Gregorian calendar was introduced had less than 365 days and less than 52 weeks.) Proof: Per definition, the first week of a year is W01 and consequently days before week W01 belong to the previous year and so there is no week with lower numbers.
Considering the highest possible week number, the worst case is a leap year like 1976 that starts with a Thursday, because this keeps the highest possible number of days of W01 in the previous year, i.e. In this case, the Sunday of W52 of the worst case year is day number 4 51*7=361 and 361-366=5 days of W53 belong still to this year, which guarantees that in the worst case year day 4 (Thursday) of W53 is not yet in the next year, so a week number 53 is possible.
An abbreviated version of the year and week number like is sometimes useful as a compact code printed on a product that indicates when it has been manufactured.
Note: The ISO standard avoids explicitly stating the possible range of week numbers, but this can easily be deduced from the definition.