User blog comment:Nayuta Ito/Trying to Make a Continuous Psi Level/@comment-30754445-20171226045826/@comment-25337554-20171228084041

At least you can continue up to 10^^10 or something, but if you go further you really need a way to express continuous tetration, not just using exponents and psi function.

Also, the Letter Notation is the most "common" way to make tetration continuous, so I don't think it's a problem...