User blog comment:B1mb0w/Rule 2B/@comment-5529393-20160207015116

You cannot argue that zeta_1 means something other than the agreed upon definition. What you can do is define your own function, where you can make any choices you wish.

You're trying to argue that the standard definition is "circular logic" by making a chain of equalities that arrives at the beginning, but that is no big deal. I can do the same thing:

4 = 3+1 = 2+2 = 2*2 = 2^^^^2 = 16/4 = 4

There's no problem with that.

Elsewhere you have said the equality epsilon_{zeta_0+1} = zeta_0 ^^ w was "correct and obvious", as some sort of knock on it, but clearly being correct and obvious is a good thing?