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What is the link between set theory, number theory and group theory. What is the added value in knowing that for example the rotations of an equilateral triangle have the same group structure as the integers mod 3.

kjell cools
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    This is waaaaaaaaay to broad. The group theory plays a role in pretty much every mathematics you can think of. You want to add and subtract numbers? Groups. You want to compose and invert functions? Groups. Pure topology can live without groups, but not much can be done without them (see: homotopy, homology, cohomology groups, etc). – freakish Feb 17 '21 at 13:49
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    The particular example of rotations has a wide application in chemistry for example. That's because some physical properties of molecules are closely related to the structure of rotations of that molecule. This gives us quick and simple method of determining some physical properties of a molecule. – freakish Feb 17 '21 at 13:57
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    For "real world applications" see this post among others. The helicopter view is almost the same as for the question "what is the added value of calculus or linear algebra". – Dietrich Burde Feb 17 '21 at 14:13

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