I was recently reminded of this post on a blog I read, *Math with Bad Drawings*. The Kaufman decimals are like the infinitely-repeating decimal expansions of rational numbers (e.g., ⅓ = 0.33333…, also notated 0.3 or 0.(3)), but where there can be more digits after the end of the infinitely-repeating part, and also more infinitely-repeating parts and infinitely-repeating parts inside infinitely-repeating parts. See the original post for details.

The article presents the question of whether it's possible to order the decimals; that is, do < and = work as expected? Here's my program to attempt to order them.

Type in some decimals below. Use parentheses (), brackets [], or braces {} to enclose infinitely-repeating portions; e.g., 0.(3) for 0.3333333….