Sets for the CSET Math
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Excerpt from the CSET Math Study Guide
Let’s review Sets for the CSET Math.
Any collection of objects as (a) the points of a given line segment, (b) the lines through a given point in ordinary space, (c) the natural numbers less than ten, (d) the five Jones boys and their dog… will be called a set or class. The individual points, lines, numbers, boys and dogs… will be called elements of a set. Generally, sets will be denoted by capital letters and elements of sets will be denoted by small letters.
Let A be a given set and let p and q denote certain objects. When p is an element of A, we shall indicate this fact by writing p Î A; when both p and q are elements of A, we shall write p, q Î A instead of p Î A and q Î A; when q is not an element of A, we shall write q Ï A.
For convenience, we shall reserve the following symbols for number sets:
N = the set of all natural numbers
I = the set of all integers
Q = the set of all rational numbers
R = the set of all real numbers
Example
1 Î N and 205 Î N since 1 and 205 are natural numbers; 1/2, -5 Ï N since 1/2 and -5 are not natural numbers.
Alan Hodgkinson of Bath University in England describes sets this way. It is useful in maths to have a diagram that visualises data on sets and groups. The following example shows an example of this for a simple case:
In a class of children at school, each child can play a maximum of two sports.They have the options of football, rugby, swimming or hockey. However any childwho plays hockey cannot play any other sports due to there not being enough time.
F represents those who play football
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