A laser is suspended 1 metre above an infinite plane. The laser swivels on its aperture, which remains at point A. The aperture is directly above point B. The laser shines a infinitely small dot onto point C. We'll call the angle BAC θ, and the distance BC d. Therefore, d = tan θ.
As θ approaches 90°, d approaches infinite. In other words, the dot starts from B, and keeps moving along this plane. Since it moves an infinite distance, it is moving forever away from B. Since it is moving forever on this plane, θ never reaches 90°, and the laser dot never comes off the plane (after all, why would the dot continue going along this plane and suddenly come off it?).
From the above 'proof', the laser could never go past 90°. Yet reality contradicts this: anyone can grab a laser pointer and lift it past 90°; physically a laser wouldn't have a purely theoretical force stop it from moving past 90°.
So, what is wrong with the above proof? If there is a fallacy, please make close reference to exactly when and how the dot parts with the plane and ceases to exist.
Note: Assume the light emitted from the laser instantaneously arrives at its endpoint on the plane.