Can a person jump 1 inch off the ground? Sure.
Can a person jump 1 inch plus 1/1000th of an inch? Sure.
Can a person jump 1 inch plus 2/1000th of an inch? Sure.
Repeat this forever. You may hit a world record, you may hit a range where it’s not likely. But you never cross a border of impossibility. So if a person can jump xx inches, then they could also jump xx + 1/1000th inches. Why not? It’s such a minuscule difference it can’t be impossible.

At some point you’ll be at a totally impossible distance like 10 feet which you know to be impossible. But nowhere in your list can you draw the line. So from one way of thinking it’s possible, but the odds get less and less each time. From another practical standpoint it’s completely impossible.

Here, however, you really just have a semantic issue. Technically, nothing that doesn’t violate the basic laws of physics is impossible, just extremely improbable. It’s just a matter of definition what level of improbability you decide to designate as “impossible.”

From a practical point of view, you could in theory calculate the total amount of muscular energy available in a person’s legs with respect to the person’s weight under the Earth’s gravitational field. That would give you the theoretical limit of a jump based on the constraints of physics.

I don’t see the dilemma here. Perhaps you can’t reach infinite precision, but you can certainly set a range of possibilities. Why can’t it be a statistical average with a margin of error, something like “People can’t jump more than 8 feet, 2 inches +/- 385/1000th inches”?

As people excell in things ,such as jumping for instance, over time, they will approach, but never reach the limit of physical impossibility. As they near that limit it becomes nessary to measure their results with increasing precision. At some point 1/1000 th of an inch won’t be considered a minuscule amount anymore , just like runners are now measure in thousandths of seconds ,etc