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Beyond + and -
(05/28/2014, 04:33 PM)JmsNxn Wrote: I used to think about trying to generalize arithmetic operations like negation and addition. I never came to three but I did come up with the following operator that I thought was very interesting:

which is holo in and by doing a little calculus that I'm too lazy to do atm ^_^.

It has the cool property


Then we define a nice metric:

so that

Now we see we can start talking about calculus even because this operator is continuous.

I always liked the box derivative:

and general box analysis ^_^

This may be a little off topic, this thread just reminded me of this.

Notice this is just the generalized distributive property with r = -1 :

And also the box derivative is known to me.
Reminds me of the " q-derivative ".



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