Sets.

  1. Only finite sets may be represented in ISETL. The elements may be of any type, mixed heterogeneously. Elements occur at most once per set.

  2. The order of elements is not significant in a set and printing the value of a set twice in succession could display the elements in different orders.

  3. OM

    may not be an element of a set. Any set that would contain

    OM

    is considered to be undefined.

  4. An expression, or several expressions separated by commas, and, in either case, enclosed in

    {}

    evaluates to the set whose elements are the values of the enclosed expressions.

  5. The empty set is denoted by

    {}

    .

  6. There are syntactic forms, explained in the grammar, for a finite set that is an arithmetic progression of integers, and also for a finite set obtained from a set former in standard mathematical notation.

    For example, the value of the following expression

    
        { x + y : x in {-1,-3..-100}, y in {-1,-3..-100} | x /= y};    
    

    is the set of all sums of two different odd negative integers larger than -100.