User blog comment:PsiCubed2/Mashimo Scale vs Letter Notation/@comment-3427444-20170807154254/@comment-77.127.24.113-20170807162202

For now :-)

Perhaps I'll use this opportunity to define Q and beyond for real numbers.

One way to do it, is to simply extend the lexicographic method to ε₀:

Q2 – 2 = [ωω 2 ]10

Q2 – 1 – 2 = [ωω×2]10

Q2 – 1 – 11 = [ωω+1]10 = [ωω×10]10

Q2 – 1 – 10 – 2 = [ωω×2]10 =  [ωω+ωω]10

Q2 – 1 – 10 – 11 = [ωω+ω1]10 =  [ωω+ω]10

Q2 – 1 – 10 – 102 = [ωω+2]10

Q2 – 1 – 10 – 101 ▪ 3 = [ωω+2]3 = [ωω+1][ωω+1]10

Q2 – 1 – 10 – 101 ▪ 2 – 2 = [ωω+1][ωω+1]2 = [ωω+1]P10

Q2 – 1 – 10 – 101 ▪ 2 – 1 – 2 = [ωω+1]P2 = [ωω+1]N10

Q2 – 1 – 10 – 101 ▪ 2 – 1 – 1 – 2 = [ωω+1]N2 = [ωω+1]M10

Q2 – 1 – 10 – 101 ▪ 2 – 1 – 1 – 1 – 2 = [ωω+1]M2 = [ωω+1]L10

Q2 – 1 – 10 – 101 ▪ 2 – 1 – 1 – 1 – 1 – 2 = [ωω+1]L2 = [ωω+1]K10

Q2 – 1 – 10 – 101 ▪ 2 – 1 – 1 – 1 – 1 – 1 – 3 = [ωω+1]K3 ~ Mashimo(67)

(assuming the approximation on the original Mashimo page is correct)

And turning the above string into a decimal we get:

Q2 – 1 – 10 – 101 ▪ 2 – 1 – 1 – 1 – 1 – 1 – 3 ≈

Q2 – 1 – 10 – 101 ▪ 2 – 1 – 1 – 1 – 1 – 147712125471966243729502790325512 ≈

Q2 – 1 – 10 – 101 ▪ 2 – 1 – 1 – 1 – 11694161473730147366852738257396 ≈

Q2 – 1 – 10 – 101 ▪ 2 – 1 – 1 – 10679690863086716881861239271002 ≈

Q2 – 1 – 10 – 101 ▪ 2 – 1 – 10285586816814250073527764628684 ≈

Q2 – 1 – 10 – 101 ▪ 2 – 10122290742547823614805152676188 ≈

Q2 – 1 – 10 – 101 ▪ 20052788073919311437368005760179 ≈

Q2 – 1 – 10 – 1010016377932734475715360781794 ≈

Q2 – 1 – 10004328416147139638914301660934 ≈

Q2 – 10001879400536038406476192411483 ≈

Q2.0000816

And using this method we could find Q values for the Mashimo Scale up to M(74).

But I hesitate to actually define Q in this way, because such a definition tends to result in lots of zeros after the decimal point. I'm still hoping to find a smoother and more practical definition for Q and beyond.