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  • $\begingroup$ I am still parsing this answer, but I think I understand the gist. Since the minimum, unitary variation of $N$ is so extremely small compared to the amount of particles we have, even though $N\in\{0,1,2,\dots,X\}$ is discrete in reality, it is okay to view it as living on the interval $[0,X]$. Since our resolution is macroscopic, varying $N$ by integer values looks the same to us as though it were varied continuously? $\endgroup$ Commented Nov 18 at 16:58
  • $\begingroup$ @Anna, you got the point. $\endgroup$ Commented Nov 18 at 17:00