There are people here who know stuff about math, right? Could I ask someone to help me understand something I'm just not getting? I posted a question (https://math.stackexchange.com/questions/3349594/are-the-definite-and-indefinite-integrals-actually-two-different-things-where-i) on stackexchange but all that's resulted in is conversations in the comments going in circles.
@trwnh Now I have more questions, because isn't a function itself a... "prime object" i guess, i don't know the right word for it, the same class of objects as values
@trwnh but what i'm not getting is that the "sin" of "sin(π)" is still the exact same "sin" as "sin(x)". you don't call it "the definite sine"
@trwnh So how is the situation with the definite and indefinite integrals any different, though?
@trwnh And that's the question I'm trying to get answered. Why do people seem set on considering the definite integral something intrinsically different from the indefinite integral?
@trwnh The whole impetus for me asking that question was in response to this other question (https://matheducators.stackexchange.com/questions/17051/a-different-symbol-for-the-indefinite-integral-antiderivative) that someone seems very intent on making absolutely certain that students understand the two to be distinct things
@trwnh i'm not sure what you're meaning to get at here? They give you two different results but are the same function
@trwnh or meta-function as the case may be. there's probably a proper math term for that. was it functor or something?
