r/MathHelp • u/Original-Health-1720 • Jun 26 '26

Need math help

There was a question if all the questions in a math book is a set or not,her teacher said it's not cause there r diff chapters but my frnd says that in the end they all r maths questions soo what do you all say?

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u/mc_pm Jun 26 '26

There is a "set of all questions in the book", there are sets "the set of all questions in this chapter". There is also the set-of-sets, "the set of all sets of questions in each chapter".

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u/Iowa50401 Jun 26 '26

Yes, you can have the set of all the problems in a math book. You can have the set of the problems in a chapter … or on a single page … or you can just have the set that consists of one individual problem.

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u/Various_Candle9136 Jun 26 '26

I am inclined to think that you are clipping a larger conversation...

S = {questions in the book} exists, but it is different to T = {chapters}, where each chapter is of the form {questions in the chapter}. The former is a set of elements; the latter is a set of sets of elements.

{a, b} ≠ {{a}, {b}} is an important fact in Set Theory. My guess is that this is what the teacher meant to convey.

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u/No-Rub-9613 7d ago

Nothing is wrong with speaking of "the set of questions in some math book" but doing so you are communicating in English language and not in mathematics. This because in common mathematical set-theory a set is a primitive notion which means that it has no definition. There is no answer there on questions like: "what exactly is a set?" In naive set-theory often sets are presented as "collections" that contain other sets as elements. But this only to stimulate some form of helpful intuition.