An interesting weather question?

Claim: At any given moment, there is a spot on Earth where there is no wind.

Proof: ??

For those who already know the proof, try to think of other applications of this rather flexible little idea. Another one I like is the fact that there is always a point somewhere on Earth's surface where the temperature is the same at that point and at the point on exactly the other side of the Earth (the antipode).

For a greater challenge, think about the set of points where the wind is not moving and see if you can say anything about that set over time (ie, from moment to moment).

(Also, I'm ignoring artifical vacuums, inside sealed houses, whatever. I just want to think of the atmosphere as a connected set.)