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To be honest, mathematics is largely a matter of recognizing what can be replaced by some other what. That the expression \(* -1 -1)\ can be replaced by the expression \1\ is just a random fact. It can also be replaced by \(- 6 5)\ and \(- 6 5 0)\ etc.

Explanations can help, but at some point it's just arbitrary. And treating mathematics at the mechanical level is a very useful abstraction, in my opinion.

I'll add that the way we teach it is pre-computer era. Playing around with something like J is a whole new post-computer age world.

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