I am very unclear what less or greater means in context of a dimension

I was thinking of set containment, but yeah, looking again, it'd be confusing for users.

I agree less than etc aren't needed. I also don't think add or sub are worth including - I don't see when you'd need to do that. I think users should only need to multiply/divide/pow and eq/ne.

pint's UnitsContainer has:

from that list I think we'd want

 '__contains__',
 '__eq__',
 '__getitem__',
 '__iter__',
 '__len__',
 '__mul__',
 '__ne__',
 '__pow__',
 '__rmul__',
 '__rtruediv__',
 '__truediv__',

actually I'm not sure on whether the dict methods should be included '__contains__', '__getitem__', ... as a list or tuples of (dimension, exponent) pairs could be an implementation. a dict can't store strain [length]/[length]

what would the semantics be for __iter__ and __len__?

Many pint methods are to support pint's specific structure where everything is composed and it computes via an internal state dict.

I personally like having the full set of arithmetic operators because then you can write elegant code where an operator callable can be applied to the dimension the same as the higher-level object.

def apply_op(op, x1, x2):
    ...
    result_dim = op(dim1, dim2)
    ...