My question is about when the statement has a potential of inclusivity, for example a statement like "It's either day time or night time" will obviously be exclusive as it's a logical contradiction if we are in day time and night time simultaneously, however I have realized that when there is potential of inclusivity then it's kind of an assumption that our statement is inclusive.
For example: The definition of the union of sets is considered inclusive, etc...
Is that always an assumption we can make (that when there potential for inclusivity then the statement is inclusive) or we will have to see what the author states? (for example in some books the definition of the union of sets is explicitly mentioned to be inclusive, in others no)
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$\begingroup$Short answer: Yes.
Longer answer: The mathematical logical operator $\lor$ is by definition inclusive. In spoken and written "natural" language, a mathematitian will almost always mean $\lor$ when they say "or", to the point when they speak of exclusive or, they will almost always explicitly say that they are.
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