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To derive "The XOR trick" I think both associativity and communitativity are needed. That is, one should also prove a ^ (b ^ c) = (a ^ b) ^ c. Instinctive, b

To derive "The XOR trick" I think both *associativity* and communitativity are needed. That is, one should also prove a ^ (b ^ c) = (a ^ b) ^ c. Instinctive, but non-trivial.

kavouras 1y ago
Yeah that's what I was thinking, you need both
- OjotCewIo 1y ago
  yep, you need both; and in fact the definition includes both: https://en.wikipedia.org/wiki/Abelian_group https://en.wikipedia.org/wiki/Abelian_group