Set Notation

Set Notation

1. set notation:

   • a collection of things
     • each item in a set is called an “element” or member
     • written in curly brackets { }
   • soccer = {alex, casey, drew} tennis = {drew, jade, hunter}
     • soccer u tennis = {alex, casey, drew, jade, hunter}

2. interval notation

   • ( ] → not including integer, is including integer
   • ( ) → not including integer
   • [ ] → is including integer

3. different notations:

   • numbers
     • N - natural numbers
     • Q - rational numbers
     • R - all rational/irrational numbers
     • Z - integers
   • unions, elements, subsets
     • unions
       • ∪ - union
       • ∩ intersection
     • elements
       • ∅ -null set, no elements
       • ∈ - is an element of
       • ∉ - belongs to
     • subsets:
       • ⊂ - is a proper subset
       • ⊄ - is not a proper subset
       • ⊆ - is a subset
       • ⊊ - is not a subset
   • extras:
     • ∶ and| - such that
     • ∴ - therefore
     • ∋ - contains
     • ∀ - for all
     • # -order or cardinality of a set
     • ∃ - there exists
     • A' or A∁ - complement of A

4. number lines:

   • o → hollow circle = doesn’t include the integer
   • • → filled in circle = includes integer
   • divide or multiply with - = flip the sign <>

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