Set Theory

• Set


  A collection of objects/elements, using the curly brackets '{}'
• Elipeses


  3 dots to represent ongoing collection
• N

  Counting numbers
• Z

  Counting numbers + Negative numbers
• Q

  Rational Numbers = Counting + Negative + fractions + decimals numbers
• R

  All real numbers + surds and pi
• ∈ (is an element of)

  If A={1,2,3}, then 2∈A
• ⊆ (is a subset of)


  If A={1,2,3,4} and B={1,2}, then B⊆A
• ⊇ (is a superset of)

  If A={1,2,3,4} and B={1,2}, then A⊇B
• ∩ (the intersection of)

  If A={1,2,3} and B={2,3,4}, then A∩B={2,3}
• ∪ (the union of)


  If A={1,2,3} and B={2,3,4}, then A∪B={1,2,3,4}
• \ (excluding)


  If A={1,2,3} and B={2,3,4}, then A\B={1}
• ∅ (the empty set)

  If A={1,2,3} and B={4,5,6}, then A∩B=∅
• ∃ (there exists)


  If x∈R, then ∃y∈R|y>x
• ∀ (for all)

  ∀x∈Z, x

  2

  ≥x
• ∋ (such that)

  A={x|∃a,b∈Z,(b≠0∧bx=a∧a⊥b)}, then A=Q