User blog comment:QuasarBooster/Googology in Geometry/@comment-35470197-20191123001017/@comment-24923514-20191123005458

> Do you mean that you are considering all constructible numbers?

That's exactly right, I just worded it differently to emphasize their relationship with rational numbers.

> 1/(almost integer - integer)

This could actually be a way of constructing longer distances than my squaring strategy. If an "almost integer" takes just a few steps to construct then it makes a good candidate.