---
tag: 0EZ758XE73
kind: definition
name: Element
msc: ["03E20"]
defines: 0QM0T7T3PZ
uses: [0SJ3RX9TXA]
sources:
  - url: https://en.wikipedia.org/wiki/Element_of_a_set
    locator: lead section
---

## Definition

Let $A$ be a [[set|0SJ3RX9TXA]] and let $x$ be an object.
The object $x$ is an element of $A$, written $x \in A$, when $A$ contains $x$.
Otherwise, $x$ is not an element of $A$, written $x \notin A$.
The proposition $x \notin A$ is the negation of $x \in A$.

## Remarks

Other phrases for $x \in A$ are "$x$ is a member of $A$", "$x$ belongs to $A$" and "$x$ is in $A$".
For $A = \{1, 2, 3\}$, $2 \in A$ and $4 \notin A$.
An element of a set can itself be a set: $\{1\} \in \{\{1\}, 2\}$, but $1 \notin \{\{1\}, 2\}$.

## Explanations

### L1 human

The symbol $\in$ asks one yes or no question: is this object in the set?
For the set of even numbers, $6 \in$ the set and $7 \notin$ the set.