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 an infinitesimal number?
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$\begingroup$ Possible duplicates: How to treat differentials and infinitesimals? , Rigorous underpinnings of infinitesimals in physics and links therein. $\endgroup$– Qmechanic ♦Commented Jul 11, 2020 at 15:08
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$\begingroup$ You will understand the difference between zero and infinitesimal by learning rigorous mathematical analysis. In short, zero $0$ is specific a real number, while infinitesimal is the process of taking limit approaching zero, which is not a number. $\endgroup$– XenomorphCommented Jul 11, 2020 at 15:13
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$\begingroup$ If you say the string has a mass dm and solve the problem, the result will depend on dm. But as you take the limit dm -> 0 in that solution, the result should match the mass = 0 solution. (That no doubt assumes certain mathematical properties of the solution with dm which I'm not qualified to comment on). $\endgroup$– Not_EinsteinCommented Jul 11, 2020 at 15:20
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A big difference is the fact that you can divide a number by an infinitesimal number. You can't divide a number by zero. So certain terms are sometimes excluded in certain equations because of this fact.
