Background on OOFP 2025-26

Set, list, tuple

Mon, 01 Jan 0001 00:00:00 +0000

Set, list, tuple #

Set #

A set can be (informally) viewed as a collection of elements with no duplicate and in no specific order.

Examples.

$\{2,5\}$ and $\{5,2\}$ are the same set,

$\{2,5,2\}$ is not a set.

Power set #

Definition. The power set $\mathcal{P}(X)$ of a set $X$ is the set of all subsets of $X$.

Function

Mon, 01 Jan 0001 00:00:00 +0000

Function #

A function $f\colon X \to Y$ maps each element $x$ of its domain $X$ to an element $f(x)$ of its codomain $Y$.

Terminology. A function is also called a map.

Examples.

$\ $the function $f\colon \mathbb{Z} \to \mathbb{N}$ defined by

$\qquad f(x) = x^2$

$\qquad$maps each integer to its squared value.
$\qquad$For instance,

$\qquad f(3) = 9$

$\ $the function $g\colon \mathbb{N} \to \mathcal{P}(\mathbb{N})$ defined by

$\qquad g(x) = \{y \mid y \in \mathbb{N},\ y < x\}$