User blog comment:Rgetar/Idea for FGH for larger transfinite ordinals/@comment-35470197-20190702232339/@comment-32213734-20190708053237

> Is it a function

Yes, it is a function, not "α[n]" string.

α[n0][n1][n2]...[nk] are FGH expressions, but α here is some fixed "large" FGH expression, and "α[n0][n1][n2]...[nk] > α[n0][n1][n2]...[mi] for any mi < ni, i < k" condition is for uniqueness (let there are many "α[n0][n1][n2]...[nk]" strings, corresponding to the same FGH expression for some fixed α, then choose of them strings with minimal n0, then choose of them strings with minimal n1, then choose of them strings with minimal n2, ..., and the result will be one unique string), so each FGH expression here uniquely corresponds to some "α[n0][n1][n2]...[nk]" string.

> The first inequality is an opposite inequality.

Thanks, fixed.