Four Basic Concepts In Mathematics

Four Basic Concepts In
Mathematics
Set Theory is the branch of mathematics that studies sets or the mathematical science
of the infinite.

 The study of sets has become a fundamental theory in 1870.
 Introduced by George Cantor (German Mathematician.)

SET

 is a collection of well-defined objects.
 usually denoted by capital letters of the alphabet and its members are enclosed with
brackets.

Elements – are the members or objects of the set which is denoted by a symbol ( ∈ ).
Example of a set:
A-{ x/x is a set of letters from the word Pneumonia}
This is read as A is the set of all x such that x is a set of letters from the
word Pneumonia.
The elements of this set are a, e, i, m, n, o, p, u.
TWO WAYS OF REPRESENTING A SET

1. ) Roster Method (Tabulation Method) – when the elements of the set are
enumerated and separated by a comma.

Ex. A={ 23, 25, 27}
Write the following Set in Roster Method

1. A={x/x is a positive integer less than 10}

A= { 1, 2, 3, 4, 5, 6, 7, 8, 9}

2. B={x/x is a month in the calendar}

B= { Jan, Feb, Mar, Apr, May, Jun, Jul, Aug, Sept, Oct, Nov, Dec}

3. C={x/x is an integer , 1< x < 8 }