ge4

• axiom of extension

  • a set is determined solely by its members
• Bilateral symmetry

  • a symmetry in which the left and right sides of the organisms can be divided into approximately.
• Radial Symmetry

  • similar parts are arranged in a balanced way around the center of the body.
• Fractals

  • a never-ending pattern found in nature
  • the pattern itself repeats over and over again at different scales.
• Spirals

  • first describe by RENE DESCARTES and was later investigated by Jacob Bernoulli
  • a curved pattern that focuses on a center point and a series of circular shapes that revolve around it.
• Tessellation is the distinct shapes are formed from several geometric unit shapes that fit together with no gaps that formed united pattern.
• Set is simply a collection of objects that can be accessed by a variable.
• Roster Method

  • writing all the elements inside the curly braces, especially when the set has finite number, of elements.
• Rule Method (Set-Builder Notation)

  • describing the elements by its property that is necessary for membership, especially when a set is compose of a large finite set or an infinite set.
• N - natural numbers

  Z - Integers

  Q - Rational numbers

  R - real numbers

  I - Imaginary numbers

  C - Complex numbers

  W - Whole numbers
• Universal Set (U)

  • a set that contains all the elements of a given set.
• Empty Set

  • a set with no elements
  • also known as the Null Set.
• Subset

  • a basic relation between sets
• Proper Subset

  • a subset which contains fewer elements of its parents set.
• Cardinality of Sets

  • the number of elements in a given set
  • denoted by |S| where S is a set
• Power Set

  • a set that includes the empty set and the original itself
  • usually denoted by P
• Union of Sets

  • the set of all elements in the collection
• Intersection of Sets

  • set of all elements that belongs to both A and B
• Complement of a Set

  • the set of all the elements in the given universal set(U) that are not present in that specific set.
• Set Difference

  • subtracting the elements from a set which is similar to the concept of the difference between numbers.
• Ordered pairs

  • a pair of formed by two elements that are separated by a comma and written inside the parenthesis.
• Cartesian Product

  • the product of any two sets, but this product is ordered
• Relation is a subset of a Cartesian Product.
• Function is a special kind of relation
• • Squaring Function f from R to R

  Formula: f(x) = x²

  - no matter what a real number input as substitute for x, the output of f is it's square.
• • Successor Function g to Z to Z

  Formula: g(n) = n+1

  -the output g is always plus than 1 to whatever the real number is being substituted in (n).
• • Constant Function h to Q to Z

  Formula: h(r)=2 for all rational number r

  -whatever rational number r might be the output would always be 2