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Did you think that I meant you can switch them on one side of the equation but not the other?

That's not what anyone is saying.



No, of course not.


But that's literally what you just did in your example.


I did not show the right side at all, so I am not sure how you can make that statement.

The point is that a+b is symmetric in a <-> b and a-b is anti-symmetric. Both left and right side are anti-symmetric.




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