This is the new hyperoperator, called Circlation. We introduce the new symbol, ○, which grows faster than up-arrows! Instead of only accepting 2 numbers, circlation accepts 2 2-entry arrays.

  1. [a,b]○[1,1]=a+b
  2. [a,b]○[1,y]=[a,a]○[b,y-1]
  3. [a,b]○[x,y]=[a,[a,b]○[x-1,y]]○[1,y]

Then, circlation would reach a growth rate of w.

But wait! There more!

We can apply up-arrows to []:


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