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What is the difference between zero and an infinitesimal number?

In a standard Atwood machine physics problem, the string going over the pulley is considered massless. So does that imply mass = 0 or mass = dm? General question: what is the difference between 0 and ...
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Making the sloppy time-reversal transformation precise

I'm reading Harbovsky and Susskind's The Theoretical Minimum Vol I. In Lecture 3: Dynamics, under Aristotle's Law of Motion is mentioned Aristotle's (fallacious) law $F(t) = m {dx\over dt}$. Later, ...
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