Functions and Relations
We can relate numbers to other numbers in tons of different ways. You've been using relations and functions to 'get from' one set of numbers to another for a while: every time you see an expression like x + 7 or sin(y), that's a function. The x and y are the input of the function, and the + 7 or sin() tell you how to get to the output.
In the next few lessons, you'll learn more about the rules of functions and relations, and how we can prove statements about them.
Topics
- definitions: functions, relations, domain, codomain, and range
- function composition
- the 'jections: injection, surjection, bijection (one-to-one, onto, and invertible)
- pigeonhole principle
Resources:
- Sections B2 & B3 from Introduction to Algorithms, Third edition.
- Discrete Mathematics: An open textbook section 0.4