User blog comment:Simplicityaboveall/The Construction of Extremely Large Numbers/@comment-24920136-20160725013617/@comment-24920136-20160725173625

Nope, 10^10 = ω^ω  does not hold in his original definition of set K

Even though in page 5 he claims

10^10 = ω^ω

10^^10 = e_0

the actual values are (from how K is defined)

10^10 = ω^10

10^^10 = ω^(10^^9)

He would need to formally word in the definition of set K otherwise the vaguely defined form

(1,2,...9,ω,ω+1,ω+2...ω+9,ω2...)

caps out at ω^ω