User blog comment:Syst3ms/YAUD/@comment-30754445-20180810132619/@comment-30754445-20180811195408

@Rpakr

"You wrote "You require them to have exactly the properties of the actual cardinals I and M" but that is only true when you assume cof(α) means the cofinality of α and α[β] means the βth term in the fundamenta sequence of α."

Because that's what these terms mean.

Why use these terms at all, if you don't expect them to behave exactly as their ordinal counterpart? Why create an entire complex structure that is written as if it is precisely something we are all quite familiar with, and then claim it is something else?

Either these "things" are supposed to behave like ordinals, in which case it makes no sense to deny that that they are ordinals.

Or they are supposed to behave in some other way, in which Syst3ms is being deliberately confusing when he is notating them as ordinals (and the question still remains, why would anyone thin that such a system would have any resemblence to Username5243's original idea, which most definitely uses ordinals).