The following cmavo are discussed in this section:

Having said so much about masses, let us turn to sets. Sets are easier to understand than masses, but are more rarely used. Like a mass, a set is an abstract object formed from a number of individuals; however, the properties of a set are not derived from any of the properties of the individuals that compose it.

Sets have properties like cardinality (how many elements in the set), membership (the relationship between a set and its elements), and set inclusion (the relationship between two sets, one of which – the superset – contains all the elements of the other – the subset). The set descriptors le'i , lo'i and la'i correspond exactly to the mass descriptors lei , loi , and lai except that normally we talk of the whole of a set, not just part of it. Here are some examples contrasting lo , loi , and lo'i :

The mass of rats is small because at least one rat is small; the mass of rats is also large; the set of rats, though, is unquestionably large – it has billions of members. The mass of rats is also brown, since some of its components are; but it would be incorrect to call the set of rats brown – brown-ness is not the sort of property that sets possess.

Lojban speakers should generally think twice before employing the set descriptors. However, certain predicates have places that require set sumti to fill them. For example, the place structure of fadni is:

Why is it necessary for the x₃ place of fadni to be a set? Because it makes no sense for an individual to be typical of another individual: an individual is typical of a group. In order to make sure that the bridi containing fadni is about an entire group, its x₃ place must be filled with a set:

Note that the x₂ place has been omitted; I am not specifying in exactly which way I am typical – whether in language knowledge, or age, or interests, or something else. If lo'i were changed to lo in Example 6.25 , the meaning would be something like “I am typical of some Lojban user” , which is nonsense.