Well, if we can, are we then now in a situation where the 'step' of 'cases' is no longer an integer sequence? That is to say, that the cases are fractional? Like, if middlecase is 0.5, then can we apply the middlecase operation again and get 0.25/0.75?
As applying cases is then just 'addition', then you can likely get the 'multiplication' and 'divisions' of the cases as applied. 'Exponentials' are just around the corner too.
Is that is the situation, that we can now get transcendental cases. The 'pi' case, or the 'e' case, pick your favorite transcendental.
More interestingly, you can then pull out the imaginary case, using Euler. e^(i*pi) = -1. Maybe that the lower-er case is just the 'e' case to the power of the 'pi' case times the 'i' case. Whatever those operations may mean.
Of course, one you're at the imaginary cases, you might as well step up into derivatives and integrals, it's just curiosity after all. Then you'll be doing partial derivatives and then Lagrangians.
Eigencase-ing comes next, and then Maxwell's equations in case format. 'Del'ing your cases should be a real trip.
After only a bit of puzzling, you're doing quantum mechanics operations with your cases, because why not?
Case-ing operations have a fruitful future for any mathematician, it seems.
Hmmm. I wonder if you can do backprop on exp(f) as efficiently as f? Then once you've learnt exp(f) you can just use exp(tf) to transform smoothly from one to the other.
