# SP18:Lecture 5 Functions

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We finished our list of proof techniques, adding implication () and existentials (). We then defined functions and discussed some examples.

# Functions

Definition: Image
If , then the image of (written ) is the set of values that are output by . Formally, or more succinctly, .

## Function examples

• we often draw functions:

The domain of is , and the codomain of is .

• another way to draw a function is with a table:
 x a 1 b 1 c 1

This almost describes a function; the domain is clearly (because if there were any other domain elements, would not be a function); and the rule is clear. However, the codomain is not clear: is it ? Or ? Or , or ? When describing a function with a table, the codomain should be specified somewhere.