Okay, so my first mathematics-related post was a bit of a letdown…but I think I’ve recovered some of my mathematical street cred (yes, mathematicians have street cred; how do you think they get into all the elite nightclubs?).

Suppose you have a function f(a, b) . I then define the “superfunction” s(f) of f(a, b) as:

s(f(a,b)) = f(a, f(a, f(a, … a))) (repeated *b* times)

Thus, s(a+b) = a * b, and s(a * b) = a ^ b, et cetera.

Consider also the “ultrafunction” u(f(a, b), c)of f(a, b) (of which the superfunction is a special case where c = 1; see below) thus:

u(f(a, b), c) = s(s(s(…f(a,b)…))) (*c* repeats)

u(a+b, 1) = a * b

u(a+b, 2) = a ^ b

s(f(a,b)) = u(f(a,b), 1)

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February 22, 2007 @ 10:38 pm at 10:38 pm

on the money again bruv