04/27/2008, 01:53 PM

In another thread I found interesting expressions (y is a result of those operations, whatever number type it may take):

y=0[0]0

y=1[1]1 = 1

y=2[2]2 = 2*2=4

y=3[3]3 = 3^3^3 = 19683

y=4[4]4=?

.....

y=n[n]n

......

y=x[x]x

......

y= i[ i]i

......

y=z[z]z

(this may be left out : y= q[q]q where q is quaternion...)

The question is, numbers 1, 2, 3, 4, ..n, ...x, i. , z .... q... are "something" - inverted hyperoperations of y.

How should we call this something and can we find these given y?

y=x[x]x, what is x if y is given and how many x will fit the equation?

Ivars

y=0[0]0

y=1[1]1 = 1

y=2[2]2 = 2*2=4

y=3[3]3 = 3^3^3 = 19683

y=4[4]4=?

.....

y=n[n]n

......

y=x[x]x

......

y= i[ i]i

......

y=z[z]z

(this may be left out : y= q[q]q where q is quaternion...)

The question is, numbers 1, 2, 3, 4, ..n, ...x, i. , z .... q... are "something" - inverted hyperoperations of y.

How should we call this something and can we find these given y?

y=x[x]x, what is x if y is given and how many x will fit the equation?

Ivars