User blog comment:B1mb0w/J Function Sandpit J 8/@comment-5529393-20160126000406/@comment-10262436-20160126093705

Hi. All three blogs cover material that is consistent. This blog elaborates the examples further to explain how the unique ordinal representation with sequence of finite integers is applied. The J_8(,n,p) function is then proposed to generate any ordinal or large number up to SVO. But only pseudo-code is offered at this time.

The examples do not answer your question in an obvious way. I will try to add an explicit example later. In the meantime, I confirm the single sequence without inner brackets suffices for the unique representation. The inner brackets are only displayed to make the construction of the sequence easier to follow.

Look at he examples  = <1,1,k,...> and  = <1,2,<1,1,2,...>,...> when the second finite integer is 1 then the sequence 'collapses' and the next integer will represent the entire third element. When the second integer is 2 then the sequence requires another embedded sequence of the form , which follows the same rules. In the second example, the second integer is 1 and the embedded sequence collapses and only a finite integer is required for the third element. The inner brackets help to illustrate the logic, but are not required to evaluate the sequence and construct the relevant unique ordinal.

Hope this helps.