• Discrete mathematics is often concerned with functions that map between other kinds of sets
  • such as binary strings or a set of tasks.
  • an assignment of people to teams, or of guests to hotel rooms, are also examples of functions.
• Definition
  • 

f = (U,V,G)
U = Domain
V = Codomain
G = Graph

Domain

• an element from the domain cant have more than 1 image (can have 0 tho)
  • image = value from V that the function returns → f(u) = v

Codomain

• not the range
• elements of codomain can have >1 preimages
  • preimage = element of U that when put into the function outputs the element from V
• codomain is just the list of possible values(all the employess)
  • but the function might not promote every single one of them

Graph

= subset of U x V

• the 2-tuple with a the element from U and its respective image
• if G =
  • still a function
  • the function just doesnt give any V elements with the U inputs
  • illustration
    • 
• arrow diagram
  • 
  • there is exactly one arrow pointing out of every element in the domain
  • if there are no arrows, it is still a function, because there are no counter-examples to the definition
• (Co)Domain of Definition
  • domain
    • the elements of U that have an image in V(corresponding value in V)
  • codomain/range
    • the elements of V that have a preimage(corresponding value in U)
• well-defined functions
  • 
  • range =
    • not using all the elements is fine
  • purple arrow is the one making the function not well-defined
    • there can only be one possible value from each input
• equality
  • f and g are equal if f and g have the same domain and target, and f(x) = g(x) for every element x in the domain.