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

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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).

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"?

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Discrete sets, as ℕ ℤ and ℚ, are in bijection within themselves, and the number of elements in them is Aleph (א) sub zero.

Continuum sets as ℝ or 𝕀 are not in bijection to the former ℕ ℤ ℚ, and the number of elements in them is Aleph (א) sub one.

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