If the limiting passage from discrete impulsive forces to continuous centripetal force is not rigorously justified, the reverse implication—area law entails purely centripetal force—is not deductively established but only approximated.
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Separate, individual pushes or shoves that happen at specific moments in time, rather than continuously.
limiting passage(in mathematics and physics)
A mathematical process of taking something in one form (like separate pushes) and showing it smoothly transforms into another form (like constant pulling) as you make the steps smaller and smaller.
reverse implication(in logic)
If you normally say 'A leads to B,' the reverse implication means checking whether 'B leads back to A'—going backwards through the logical chain.
rigorously justified(in logic and mathematics)
Proven with strict, step-by-step logical reasoning that leaves no room for doubt or gaps in the argument.