An instant is a point on the time coordinate axis. dt is the limit as delta t ->0. All that matters is time differences, that's why dt is used. dt is not equal to zero, but represents an infinitesimally small delta t.
Time is a dimension. The points on it's axis are instants. Points are infinitesimally small as is dt, a time difference. Instants are not mathematical artifact. These are concepts that enable the mind to grasp reality. The points <=> instants are representations and names for well defined concepts, not the actual reality.
Zeno's paradox is only a paradox, because it fails to recognize the fact that the series of "1/2 times" converges to the time it takes the arrow to hit the line. All the other terms amount to adding essentially zero magnitude corrections beyond the appropriate significant figures. So it's Zeno's concepts that don't represent reality, not the math guys.
That's right, and also Peter Lynds "point." Points, like instants, are conceptual fictions, useful in geometry and mathematics as methods, but without onotological existence.
Ontologically, no segment of anything is "infinitesimal," which is the equivalent of zero. The calculus is nothing more than a clever scheme that allows division by zero, by pretending that zero is just an infinitely small fraction. Like the imaginary roots of negative numbers, the "infinitesimal" is a very useful method, but to conclude that these fictions have actual existence is madness, a common condition of hatters and mathematicians. It was mecury vapor that caused the condition in hatters, it is reification that causes the condition in mathematicians.
Hank