It's certainly not a mathematical function. That being said, to even write 4 = x ^ (x ^ x ^ x ^ ...) is a bit misleading. The function diverges for y not in the

It's certainly not a mathematical function. That being said, to even write 4 = x ^ (x ^ x ^ x ^ ...) is a bit misleading. The function diverges for y not in the range of e^-1 < y < e. I think that's a bit simpler and elegant way to look at it. A proof can be found on page 240: http://www.maa.org/sites/default/files/pdf/upload_library/22/Chauvenet/Knoebelchv.pdf http://www.maa.org/sites/default/files/pdf/upload_library/22... (pdf)