User blog comment:Nayuta Ito/Trying to Make a Continuous Psi Level/@comment-30754445-20171226045826/@comment-30754445-20171228090620

You misunderstood me.

What I meant was that once you have a smooth psi scale from 1.0 (10) to 2.0 (E10), you can use this to define continuous tetration for all real x>1 by writing:

10^^x = psi(x) for 12

For example:

10^^74.31 = 10^10^10^....^psi(1.31) (with 73 10's)

Easy.

Just make sure that that the growth rate of psi(x) at 2 is similar to the growth rate of 10^psi(x) at 1. This means, basically, that psi(1.999) should be about 10^9.99.