User blog comment:Syst3ms/Looking for some ideas/@comment-30869823-20180526213547

Extending FGH to the real numbers is hard because but fundamental sequence and function iteration aren't defined for them.

I don't like just naming numbers for the sake of naming numbers. If you come up with a notation, sure name some of the larger values definable in it or create a system to name every number upto a very large number.

Here are some ideas I want to persue if I have time:

- A hydra ordinal collapsing function, a generalisation of hydras.

- Greater than cardinals: In OCFs al you need from a large cardinal is it being greater than any other cardinal you define.

- Generalised middle growing hierachy: extend the middle growing hierachy to produce and work with greater than cardinals.

- An array notation based on the Ackermann function and ordinal arrays (don't know how to extend it past tetrational level)

- A well-defined version of MOST

- An ordinal hierachy significantly more power than the fgh (don't know how)

- Dice rolling hyper operations

- Creating googological programs

- Busy brainf*ck hierachy

As you can see I'll never have enoug time to persue all of my idea's, for any notation I learn about I basically have a new idea. (please tell me if you would like to persue one)