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January 1st is not always on the first week of the year
(www.jpvalencia.com)
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How is that? Do you mean that week 1 can occur twice? Or is there another issue?
IIUC you can have days at the start and the end of the year that are all in week 1, and those are two different weeks. But one of those would be, let's say, week 1 year 2025, and the other would be week 1 year 2026. According to the blog post if you have a week 1 at the end of a year the ISO year number for that week is the next year.
It only happens with ISO weeks. An example is 2006. Each of the weeks belong to different years (so 2005W52 and 2006W52 are different), but each can contain days from another year. So for example Sunday 2006-01-01 is part of week 52 of 2005. Week 1 starts on January 2. Then at the end of 2006 you have another week 52, but that week is actually part of 2006.
It's a bit of a cheeky thing to point out, because at no point is a day in two different weeks, and the week itself only belongs to one year. It's just that you can't assume that any given day belongs to the same year as the week it is in. That is: 2006-01-01 is in 2005W52 not 2006W01.