User talk:Username5243/Pi notation

This seems similar to what SimplicityAboveAll has tried to do, by taking functions on natural numbers and extending them to arbitrary ordinal values. But no method is given for how one would do this in general, in a unique, canonical manner. My feeling is that this is impossible to do in general, unless you do something silly like doing the same operation on all ordinals. I think what is giving people false hope that this can always be done is that for small ordinals, there are commonly used notations, so you can just use that notation to help you pick out a particular extension to a natural number function. But, how will you do the same when there is no notation for the ordinals you are dealing with? Otherwise, you can only extend your notation up to ordinals that exist in some preexisting notation, which is not so useful. Deedlit11 (talk) 22:03, September 20, 2017 (UTC)