{"id":111258,"date":"2022-01-31T13:49:18","date_gmt":"2022-01-31T19:49:18","guid":{"rendered":"https:\/\/www.mometrix.com\/academy\/?page_id=111258"},"modified":"2026-03-28T12:24:42","modified_gmt":"2026-03-28T17:24:42","slug":"sets","status":"publish","type":"page","link":"https:\/\/www.mometrix.com\/academy\/sets\/","title":{"rendered":"Sets Overview"},"content":{"rendered":"

A set is essentially a collection of items, where each item is considered an element<\/strong>. Elements are listed inside of brackets, and as a collection, they make up a set<\/strong>. Sets are usually named using a capital letter. For example, \\(A=\\{1,2,3\\}\\) states that set \\(A\\) consists of the elements \\(1,2,\\) and \\(3\\). You know that a number is considered an element of a set if it is listed inside of the brackets. For example, \\(5\\) is an element of the set \\(T=\\{5,6,7\\}\\), but \\(4\\) is not an element of this set.<\/p>\n

Sets Sample Questions<\/a><\/div>\n

Sometimes the elements of a set will be words or items, instead of numbers. For example, we can list the elements of the set \u201cthings on the kitchen table\u201d as K={plates, cups, silverware, table cloth, water bottle, candle}.<\/p>\n

Sets are often used in algebra when writing the solutions for inequalities<\/a>.<\/p>\n

For example, the inequality \\(x \\lt 4\\) means that all values less than \\(4\\) are solutions for \\(x\\). You will often need to phrase your answer in what is referred to as \u201cset notation\u201d. So instead of saying \u201call values less than \\(4\\) are solutions for \\(x\\)\u201d, we use a consistent collection of symbols to describe the set of solutions. The solutions for \\(x \\lt 4\\) would be expressed as \\(\\{x \\mid x\\text{ is a real number and} x \\lt 4\\}\\) using set notation.<\/p>\n

Solution sets often consist of many values. Using set notation saves space and condenses the solution set into a more compact format.<\/p>\n

There are a few symbols to be familiar with when studying set notation. Here are the symbols you should be most familiar with:<\/p>\n

\\(\\{\\text{ }\\}\\) means \u201cis a set\u201d
\n\\( \\epsilon \\) means \u201cis an element of\u201d<\/div>\n

Sometimes, sets can be subsets<\/strong> of other sets. For example, the set \\(A=\\{3,4,5\\}\\) is a subset of \\(B=\\{2,3,4,5,6,7\\}\\) because all of the elements of set \\(A\\) are also in set \\(B\\).<\/p>\n

The symbol for \u201csubsets\u201d is \\(\\subset\\). This is read as \u201cis a subset of.\u201d<\/p>\n

Sometimes, sets will contain elements that are short and concise like \\(A=\\{1,2,3,4,5\\}\\). However, some sets will contain elements that are never ending. These sets are referred to as infinite sets<\/strong>.<\/p>\n

Using set notation for an infinite set is very similar to the notation for a finite set. The only difference is the use of the ellipsis (…).<\/p>\n

<\/div>\n

For example, \\(C=\\{2,3,4\\}\\) represents a finite set, but \\(D=\\{4,5,6…\\}\\) represents an infinite set.<\/p>\n

One way to think about finite and infinite sets is to think of finite sets as the factors of a number, and infinite sets as the multiples of a number. Factors are limited, but multiples can continue on infinitely.<\/p>\n

Sets Sample Questions<\/h2>\n

Here are a few sample questions going over sets.
\n\n\t\t\t\t

\n\t\t\t\t\tQuestion #1:<\/strong>\n\t\t\t\t\t

 
\nWhich of the following is an infinite set?<\/p>\n<\/div>\n\t\t\t\t\t

\\(A=\\{\\text{letters in the alphabet}\\}\\)<\/div>
\\(B=\\{\\text{Europe, Asia, Africa}\\}\\)<\/div>
\\(C=\\{…-3,-2,-1,0,1,2,3…\\}\\)<\/div>
\\(D=\\{1{,}000,2{,}000,3{,}000\\}\\)<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t