I felt pretty meh about this idea ('triangle of power') when I encountered it before. If anything, I'd keep the triangle *predicate* (x^y = z) (ditching the function symbols) & write it as a sort of morphism to avoid the *excess* symmetry that an equilateral triangle suggests
A lot of Ramanujan identities would be very hard to write in this notation. math.stackexchange.com/a/165…
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The result has a more reasonable set of essential identities: (x ->^{y} z is the symbol that means x^y = z, or equivalently, to better show off why "morphism composition" works, ln(x) * y / ln(z) = 1)
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I like this, has a nice symmetry to its representation.
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Thanks --- The fact that it has some symmetry *and not too much* seems important to me, tho. I def. agree with the 'triangle of power' proposal that notation should suggest the symmetries of what it denotes, but I think the actual proposal suggests too much!
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Replying to @jcreed
A chain of nested radicals would then just be a sequence of arrows with parenthetical subexpressions. So could write this linearly.

4:42 PM · Dec 2, 2020

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Replying to @smdiehl
yeah, I suppose that would be the following, if you allowed the leave-an-argument-out-to-indicate-hilbert-epsilon-quantification-of-it function symbols
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