[JackWilson]

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final clarification, FBD style:

wheel velocity = conveyor velocity = lim(x) as x -> infinity. this is defined by the OP and the fact that the continual (feedback) acceleration of both is inevitable.

thrust velocity + wheel velocity - conveyor velocity = net velocity

since wheel velocity = conveyor velocity, then net velocity MUST equal thrust velocity

therefore, the plane can take off, as long as thrust velocity is great enough to create lift.

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How is this still going on? Does this require a "proof"?

Here we go.

The plane's wheels are stationary. the runway is stationary, thus satisfying the OP.

there is no net air speed---> no lift.

The engine applies thrust--> wheels speed up faster than runway--> net air speed > 0

-->plane takes off.

However, wheels are moving faster than runway, so OP is not satisfied.



OH By the way, for those unfamiliar with math, infinity + 1 is strictly greater than infinity, but not by much.

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I think this part is wrong. "The runway moves in the opposite direction of the plane at the exact same speed as the plane's wheels" does not imply this.

But I'll be the first to admit that I'm no rocket scientist.