Superfunctions and Ultrafunctions

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)

Advertisements

One Response to “Superfunctions and Ultrafunctions”

  1. paul_k Says:

    on the money again bruv


Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: