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We usually talk about rotations in the clockwise or counterclockwise direction. But if a rotation is just a function defined on the space, then it is all about points and their images, and there is no "direction" involved.

For example, consider the unique rotation about $(0,0)$ that sends the point $(1,0)$ to the point $(0,1)$ in the plane. Is it in the clockwise or the counterclockwise direction ?

We could say it's counterclockwise because it's a 90° turn, but we could also say it's clockwise because it's a -270° turn. The conclusion seems then that the rotation has no direction in itself.

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An instantaneous rotation and a continuous rotation are two different things. An instantaneous rotation has no direction. It has a before and after, and that's it.

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