User blog comment:Xxmarijnw/Wezel's Number/@comment-11227630-20141208154740/@comment-2033667-20141209065827

i take back what i said, cf is right. the formal definition is W(0) = 10^10^100 and W(n+1) = W(n)^^^2, and wezel's number is W(10^10^10^100).

we can show that W(n) < 10^^^(2n+2) by induction. base case is W(0) < 10^^^2. assume W(n) < 10^^^(2n+2), then W(n+1) < (10^^^(2n+2))^^^2 < 10^^^(2(n+1)+2) by LAPL. so W(10^10^10^100) < 10^^^(2(10^10^10^100)+2).