User blog comment:Mh314159/A hopefully powerful new system/@comment-35470197-20190628050713/@comment-35470197-20190629233731

> I made a conscious decision to avoid using traditional function notation with subscripts and to use braces instead

Yeah, it is what many googologists do. I just introduced the way to use function symbols for the clarification because it will possibly help you when you have some trouble to precisely describe the rule sets such as the order of the priority of the application to substrings. If you can formally write the rule sets, then you do not need to follow the same convention.

> which I don't even know how to format in the comment section here -- where are the tools?

You can use mathjax by writing something like \([0]\[1]^{[2]}[3]_{[4]}\). It will be converted to the formula \([0]\[1]^{[2]}[3]_{[4]}\). (Sometimes FANDOM causes error to display such formulae, though.) This \( \) tag works also in the bodies of articles and blog posts.

> Would something as simple as always distributing the cycle number, as above, do the job?

Using brackets, braces, and so on is one of the simplest way to write down expression without complexity. Just it causes the difficulty to describe the whole complete rule sets. On the other hand, using function symbols causes the difficulty to write expressions, while it helps us to describe the whole complete rule sets.

Another well-known method with simple expressions is to use matrices or seprators, but it is not so easy to write down the rule sets.

> I thought that something like the distributive property for cycle numbers would be acceptable as long as it's clear what the superscripts really mean.

It is acceptable, as long as those properties are clearly declared. We are allowed both to assume the left or right distributive property and also not to assume it. (If we do not assume the left or right distributive property, we can define [2][3][4] by using new rule sets so that the system becomes stronger. Therefore it can yield a benefit.) Therefore we need to clearly declare which syntax-theoretical assumptions we actually use.

> I really should send you a case of beer for all the work you've done on this, thanks.

It is my pleasure. Since I do not drink, I prefer milk or juice :)