"There is no well-defined time zone at the North Pole".
Also: "The sun sets & rises once a year."
If you move 1 metre away from the North Pole, then the first statement is no longer true, but the second still holds.
And "time" doesn't cease to exist just because you are standing on a large spinning ball on the part of the surface of the ball that intersects with the axis of spin.
"There is no well-defined time zone at the North Pole".
Also: "The sun sets & rises once a year."
If you move 1 metre away from the North Pole, then the first statement is no longer true, but the second still holds.
And "time" doesn't cease to exist just because you are standing on a large spinning ball on the part of the surface of the ball that intersects with the axis of spin.