iso8601 - What mode for MySQL WEEK() complies with ISO 8601

Question

What mode for MySQL's WEEK() function yields the ISO 8601 week of the year? Argument 2 of WEEK() sets the mode according to this chart:

+--------------------------------------------------------------------+
| Mode | First day of week | Range | Week 1 is the first week ...    |
|------+-------------------+-------+---------------------------------|
| 0    | Sunday            | 0-53  | with a Sunday in this year      |
|------+-------------------+-------+---------------------------------|
| 1    | Monday            | 0-53  | with more than 3 days this year |
|------+-------------------+-------+---------------------------------|
| 2    | Sunday            | 1-53  | with a Sunday in this year      |
|------+-------------------+-------+---------------------------------|
| 3    | Monday            | 1-53  | with more than 3 days this year |
|------+-------------------+-------+---------------------------------|
| 4    | Sunday            | 0-53  | with more than 3 days this year |
|------+-------------------+-------+---------------------------------|
| 5    | Monday            | 0-53  | with a Monday in this year      |
|------+-------------------+-------+---------------------------------|
| 6    | Sunday            | 1-53  | with more than 3 days this year |
|------+-------------------+-------+---------------------------------|
| 7    | Monday            | 1-53  | with a Monday in this year      |
+--------------------------------------------------------------------+

Will one of these modes give the ISO 8601 week of the year?

Answer 1

In ISO week numbering, Monday is the first day of the week, so that alone narrows it down to one of the odd-numbered modes.

Per Wikipedia:

There are mutually equivalent descriptions of week 01:

• the week with the year's first Thursday in it (the formal ISO definition),
• the week with 4 January in it,
• the first week with the majority (four or more) of its days in the starting year, and
• the week starting with the Monday in the period 29 December – 4 January.

The third of those descriptions matches "with more than 3 days this year" from the table above, so now we've narrowed it down to either 1 or 3.

Finally, still from Wikipedia (emphasis added):

If 1 January is on a Monday, Tuesday, Wednesday or Thursday, it is in week 01. If 1 January is on a Friday, Saturday or Sunday, it is in week 52 or 53 of the previous year (there is no week 00).

Hence, the range must be 1-53, not 0-53. This in turn means the right mode is mode 3.