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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.