CRUD is an acronym that stands for Create, Read, Update, Destroy.
One could argue that these four actions are MECE and effectively exhaust the "manipulation space" of data. To put it more boldly: These are the only four things you can ever do with any data, period.
This is not some mathematical proof. It's a community heuristic. It's a checklist of actions that you can think through for any given resource and ask questions like: Have we implemented action A for resource R? Who can perform action A on resource R? If action A is performed, what follow-up actions should be performed? Etc.
A similar "action collection" to CRUD are the HTTP Request Methods.
- GET -> Read
- POST -> Create
- DELETE -> Destroy
- PUT/PATCH -> Update
One could conceptualise PUT and PATCH as sub-types of update: PUT is a complete overwrite, and PATCH is a partial update.