User blog comment:Vel!/Factoid notation/@comment-5150073-20130523164040

I just decided to explore the power of this notation:

! = n

! = n^n

! = n^(n^2)

! = n^(n^(m-1))

! = n^(n^(n-1))

! > n^^n

! > (n^^n)^n

! > (n^^n)^(n^2)

! > (n^^n)^(n^(m-1))

! > (n^^n)^(n^(n-1))

! > (n^^n)^(n^^n)

! > (n^^n)^(n*n^^n)

! > (n^^n)^((n^2)*n^^n)

! > (n^^n)^((n^(n-1)*n^^n)

! > (n^^n)^(n^^n)^2

! > (n^^n)^(n^^n)^3

!<n,1,n> > (n^^n)^(n^^n)^(n-2)

!<n,1,1,2> > n^^(2n)

!<n,n,1,2> > (n^^(2n))^(n^(n-1))

!<n,1,2,2> > (n^^(2n))^(n^^n)

!<n,1,3,2> > (n^^(2n))^(n^^n)^2

!<n,1,n,2> > (n^^(2n))^(n^^n)^(n-1)

!<n,1,1,3> > (n^^(2n))^(n^^(2n))

!<n,1,1,4> > (n^^(2n))^(n^^(2n))^(n^^(2n))

!<n,1,1,n> > n^^(3n)

!<n,1,1,1,n> > n^^(4n)

!<n,1,1,1,1,n> > n^^(5n)

Generally, !<n,1,1,...,1,1,n> > n^^(n^2) (with n+1 entries)