Applications of Tetration

[andydude]

I would like to address each comment you made:

mathematics is not finished ...

• Mathematics is never finished! Goedel's incompleteness theorem even proves it!
  
  

  ... is not finished, no ... which does not ...

• "Simply stated, it is sagacious to eschew obfuscation." -- Norman R. Augustine
  
  

  analytical theory of tetration can not be solved ...

• The analytical theory of tetration is coming along great with the real number line as is, but requires complex numbers for some bases. There is nothing wrong with the real number line, period. There are many things that make other systems much nicer than the reals, for example algebraic closure of the complex numbers, the transfer principle of the hyperreal numbers, etc. Also, there are many cases where definitions are extended beyond their original domains, for example but the series was only defined for . This does not mean the definition was wrong, it just means the latter is a formula with a larger domain. I recognise that is evidence that tetration pushes real numbers into the complex plane, I accept that. You need to learn to keep your cool.
  
  

  ... rebuild the real number line, complex numbers so that they fit tetration?

• If you read Henryk Trappmann's paper on binary tree arithmetic available from the top of this web site, that is pretty much what he does. He effectively re-builds the real numbers using binary trees (as far as I understand) and he does this to better fit tetration. You are not alone.
  

Andrew Robbins