Why are asymptotes in parenthesis and not brackets

Asymptotes, in mathematics, refer to a restriction at the domain set or the range set. It's drawn as a not solid line to indicate, graphically, the values that are not defined to the function.

So, when we express the domain and range sets of a function, we use parenthesis or brackets. In case of having asymptotes we use parenthesis, because that sing indicates an exclusion of the undefined value. On the other hand, the brackets indicates inclusion.

That means, if we use brackets to indicate asymptotes in an interval, that means the value is well defined for the function, which is false.

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