Ultrafunctions Revisited

I was contemplating the properties of the ultrafuncton (see the previous post), and I was wondering if there might be some higher-level version of the ultrafunction, and I realized that the ultrafunction itself is that function. For example:

u(f(a), n) = f(f(f(f(…a…))) (f applied n times)

But then, it follows naturally that

u(u(f(a), m), n) = u(u(u(…f(a)…), m), m) (ultrafunction applied n times)

So therefore, even though in many nested-function-type situations, there is an infinite hierarchy of such functions (consider Knuth’s up-arrow system), in this case, this single function fills in the hierarchy all by itself.


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 )

Google+ photo

You are commenting using your Google+ 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 )


Connecting to %s

%d bloggers like this: