An expression like n £5
is a predicate (in the variable n) or predicate over the
set Naturals. A predicate becomes an assertion whenever a value is assigned
to its variable. A value satisfies a predicate if the predicate
is true at that value:
n £5 is satisfied
at n = 5 but it is not satisfied at n = 7.
Use predicate Pred(x) to define new set NewSet from
existing set Set
NewSet = {x Î Set
|
Pred (x) } (*)
Examples
{1,2,3,4,5} = { n Î Naturals
|
n £5 }
TallStudents = { name Î Students
|
name is more than 6 feet tall}
A predicate over a set can involve an expression in any attribute of its
elements.
The variable name x in (*) is not significant--replacing x by
y
makes no difference:
{x Î Set | Pred
(x)
} = {y Î Set
| Pred
(y) }
That is why x in (*) is called a dummyvariable.