CRDTs are just a way to send to send data between parties so that all parties end up with the same thing after receiving all messages, even if they receive them out of order. The way the messages are encoded is the math part, ensuring that you can keep applying these functions to your existing state to always get to the final state. That's where the associative/commutative requirements come from.
Note that there are operation-based (sending how something should be updated) and stated-based (sending what it should be updated to) CRDTs and they have different semantics and use-cases.
CRDTs are just a way to send to send data between parties so that all parties end up with the same thing after receiving all messages, even if they receive them out of order. The way the messages are encoded is the math part, ensuring that you can keep applying these functions to your existing state to always get to the final state. That's where the associative/commutative requirements come from.
Note that there are operation-based (sending how something should be updated) and stated-based (sending what it should be updated to) CRDTs and they have different semantics and use-cases.