Sets

A set is an unordered collection of objects.

It is completely determined by what its elements are – The order in which they might be listed does not matter – Some elements might be listed more than once.

집합에 포함된 object들을 elements, member라고 부른다. 집합에 포함되는 원소인지 여부를

x ∈ S and x ∉ S 로 표현한다.

Set-roster notation(원소나열법)

Examples

• Set of all vowels in the English alphabet:

V = {a,e,i,o,u}

• Set of all odd positive integers less than 10:

O = {1,3,5,7,9}

• Set of all positive integers less than 100:

S = {1,2,3,……..,99}

• Set of all integers less than 0:

S = {…., -3,-2,-1}

Is {0} = 0?

{0} ≠ 0 because {0} is a set with one element, namely 0, whereas 0 is just the symbol that represents the number zero.

How many elements are in the set {1, {1}}?

The set {1, {1}} has two elements: 1 and the set whose only element is 1.

Important Sets