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Is there a mathematical process resembling the terms "digital"/"discrete" and "analog"/"continuous"?

I always had trouble understanding the terms "digital" and "analog"; Wikipedia and various Q&A sessions didn't contain explanations I found clear.

I understood that these terms aren't well defined in Computer Science or Physics literature but perhaps only in the "signal process" engineering field, hence not based on some formal logic theory, but it might be possible to represent them in a mathematical process (as with [Continuous or discrete variables](https://en.wikipedia.org/wiki/Continuous_or_discrete_variable)).

It might be grasped absurd but I was thinking that *addition* of *natural numbers* as with `1+1` is a "digital"/"discrete" process and that *multiplication* of *natural numbers* as with `3*2` is an "analog"/"continuous" process (because of the continuous addition of 2, three times).

**Is there a mathematical process resembling the terms "digital"/"discrete" and "analog"/"continuous"?**