> In the contexts that you mentioned, "integral" is a synonym of "integer."

Can you provide a source ? There's no mention of "integral" in the Wikipedia page of "integer" (but there's mentions of "integral element" and "integral domain" which are not synonyms for "integer".

Even if "integral" is a synonym for "integer", I think we should use "integer" or "int" in the documentation because "integral" is harder to understand as readers are searching why "integral" is used in this particular context instead of "integer".

It looks like the documentation describes the mathematical, theoretical, point of view of those functions, as supported by the PEP3141, but those functions are not theoretical, they're actual implementations returning actual integers.

I can understand the need to abstract the implementations to make the documentation more readable, we're already not manipulating bits or even bytes, there's nice abstractions of those implementations so we can manipulate `int`, `float` etc, which are also implementation we may want to abstract again and say we're not manipulating "the implementation" (like "an int") but a mathematical domain (like "a natural number"), but going all the way down to vocabulary I can't even find on Wikipedia is probably going the wrong way: The documentation is less readable this way.