s (= t
s (< t
s =) t
s >) t
To calculate the union of two sets:
s \/ t
s /\ t
s \ t
All the above three operations can be performed on any objects as well as finite sets. If both operands are finite sets, the outcome is also a finite set. If any operand is not a finite set, the result is usually a function that can be used as a set. For example, if
u = s \/ tthen u is a function such that u(x) = 1 if x is a member of either s or t, and zero otherwise.
The interpreter is capable of determining if s is a subset of t only when s is a finite set. It is done by testing each element of s. If s is defined by a function, such computation is impossible and would not be attempted. The same applies to other set operations that involve infinitely many steps of computations.
oz 2009-12-22