Set Theory explores the fundamental concepts of sets, including operations, relations, and applications in mathematics.
A function is a special type of relation that connects each element of one set (the domain) to exactly one element of another set (the codomain).
If \(f\) is a function from \(A\) to \(B\), we write \(f: A \to B\). For each \(a \in A\), \(f(a)\) gives an element in \(B\).
Functions can describe everything from how a vending machine gives snacks to how a computer translates code!
The function \(f(x) = x^2\) maps numbers to their squares.
Assigning each student to their locker number is a function.
A function matches each input to exactly one output—no repeats, no leftovers.