SETS
The basic granted, undefined concept with which we shall be concerned is that of a set. The words 'collection', 'family' or 'class' are only synonyms of the word set.According to Canter, set is a collection of definite well defined objects of perceptionor thought. Thus we can say that a set is a collection of objects called elements which are 'distinct' and 'well defined'. The elements of a set may also be called members of the set or points of the set. The sets are denoted by capital letters A, B, C etc. and their elements by small letters a, b, c etc. If a is an element of a set 4, this is indicated as a EA. The symbol E stands for belongs to' or is an element of.
There are two standard notations for designating a particular set. We list all
elements of it in a curly bracket. Thus {a, b, c} in a set of first three alphabets of English language. A cet may also be specified by stating properties which its elements must satisfy. In this case we write A = {r:P)}, where Pt) is a property concerning x. The symbol coion :or / stands for such that.
For example : A = {1,2,3) = {*:x is a positive integer and x < 4}
If a is not an element of A or a does not belong to A, we write a EA.
A set, consisting of finite rumber of clements is called a finite set.
The sets A = {5,7,9, 11} and B = {4,8, 16, 32, 64) are finite sets.
A set which is not finite is called infinite set or inother words, if number of
elements in a set is infinite, the set is called infinite set.
The following sets are infinite sets
() The set N = {1,2,3, ..of all natural numbers.
(i) The set Z = {0, t 1, +2,.. of all integers
The set Q = {x:x = , where p, q, E Z and q 0} of all rational
numbers.The set R of all real numbers.
(iv) (The set C= +iy :x,y ER) of all complex numbers.
If every clement of the set A belongs to the set B, we write A B and say
that A is a subset of B or B is a super set of A. For example, NCZSOS
RSC. Also ifA = {1, 2, 3) and 3 =fi, 2, 3, 4, 5), then A SB. Every set is subset
of itself, for example NCN, ZCZ etc. Also if A SB, we say that A is contained
or included in B or B contains A.
A set, consisting of finite rumber of clements is called a finite set.
The sets A = {5,7,9, 11} and B = {4,8, 16, 32, 64) are finite sets.
A set which is not finite is called infinite set or inother words, if number of
elements in a set is infinite, the set is called infinite set.
The following sets are infinite sets
() The set N = {1,2,3, ..of all natural numbers.
(i) The set Z = {0, t 1, +2,.. of all integers
The set Q = {x:x = , where p, q, E Z and q 0} of all rational
numbers.The set R of all real numbers.
(iv) (The set C= +iy :x,y ER) of all complex numbers.
If every clement of the set A belongs to the set B, we write A B and say
that A is a subset of B or B is a super set of A. For example, NCZSOS
RSC. Also ifA = {1, 2, 3) and 3 =fi, 2, 3, 4, 5), then A SB. Every set is subset
of itself, for example NCN, ZCZ etc. Also if A SB, we say that A is contained
or included in B or B contains A.
إرسال تعليق