User blog comment:P進大好きbot/Elementary Large Number/@comment-30754445-20181118000005/@comment-30754445-20181118123628

'''"Oh, then I would like to see it. I searched it in this wiki, but could not find it. Could you give me a link?" '''

I don't think she ever published in on the wiki. But it's easy to explain precisely how it works:

We define a 1-to-1 correspondence between the natural numbers and epsilon-0:

(a) Ord(1)=0

(b) For any integers k,n>0 and prime p:

If Ord(n)≥Ord(p) then:Ord(n×p)=Ord(n)+Ord(p)

(c) Ord(pn)=ωOrd(n) And then, Pink(n) is exacty equal to HOrd(n)(0) (H being the Hardy Hierarchy with the Weiner fundamental sequences). Of-course, emlightened did not explicitly mention either ordinals or the Hardy Hierarchy in her definition. Everything was done with elementary means. Later I created my own version based on the same idea which reached the SVO, and Emlightened herself created another one that reaches the BHO (we called them "purple numbers" and "blue numbers" respectively). "I thought (and was sometimes implicitly told) that explanations with heavy mathematics have readers eto keep away" Well, I didn't expect your explanatoin to include 2-adic integers and Godel representations! Are these things really needed to get the point across? The table of ordinals is useful, though.

"Now I updated the definitions and the explanation"

Cool!

After a quick look at the ordinal table, it indeed looks like a variation on the "pink numbers" idea. Only you seem to be using some scheme with powers of two instead of the primes.

Let me see if I got something right:

I'm guessing that ωω+1 corresponds to 33,554,433. Is this guess right?