Alright, I agree, but I don't see how that applies to the other examples. Point masses on a string are discrete; you can think of the mass density before taking the limit as the sum of delta functions, and then taking the limit replaces the sum with an integral.
The same sort of thing happens...
In math and physics, one often takes the limit of an expression involving an integer N as N → ∞, and ends up with the expression of a continuous variable x. Some examples of this are:
- An integral as the limit of a Riemann sum of N terms
- A string with continuous mass density as the limit...