Representation of a set

REPRESENTATION OF A SET:
There are three main ways to specify a set:
(1) by listing all its members(Tabulation method OR Roster form);
(2) by stating a property of its elements (Rule method OR Set builder method);
(3) by defining a set of rules which generates (defines) its members (recursive rules).

ROSTER FORM. The first way of course is suitable only for finite sets. In this case we list
names of elements of a set, separate them by commas and enclose them in braces:
Examples: {1, 2,3, 4,5}, {George,William,Ram}, {a,b,c,d}.

RULE METHOD:The method by which we list the property or properties satisfied by the elts of the set is called rule method or set-builder method.
Example: {x/x is a multiple of 3.}
Read: “the set of all x such that x is a multiple of 3”

RECURSIVE RULES. (Always safe.)
Example – the set E of even numbers greater than 3:
a) 4 belongs to E
b) if x belongs to E, then x + 2 belongs to E
c) nothing else belongs to E.
The first rule is the basis of recursion, the second one generates new elements from the
elements defined before and the third rule restricts the defined set to the elements
generated by rules a and b. (The third rule should always be there; sometimes in practice
it is left implicit.)