[olddustytrail]

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.

[davrosthedalek]

No, of course not.

[olddustytrail]

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

[davrosthedalek]

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.