# What does “∈” mean?

I have started seeing the "∈" symbol in math. What exactly does it mean?

I have tried googling it but google takes the symbol out of the search.

• It means "belongs to". For instance $x\in A$ means that the element $x$ belongs to $A$. – Stefan Hansen Jun 25 '14 at 5:27
• By pure coincidence I was just searching how to input this symbol in mathjax! – Chinny84 Jun 25 '14 at 5:34
• You could try googling "mathematical symbols"... – user147263 Jun 25 '14 at 5:46
• Google doesn't support this at the moment, but Wikipedia does. Enter it in the search or put it in the URL. Take these examples: , and . – Steve Klösters Jun 25 '14 at 9:47
• $8$ up votes for this :O – user87543 Jun 25 '14 at 11:41

$\in$ means '(is) an element of'

For instance, 'Let $a\in A$' means 'Let $a$ be an element of $A$'

• Being only a freshman going into Honors Algebra Two, I don't understand the concept. But thanks for the answer, even if I don't understand the concept at least I know what it means. – Locke Jun 25 '14 at 5:31
• @Locke Look at the link I added too – Hippalectryon Jun 25 '14 at 5:32
• Thanks for the link. The information on that Wiki really cleared it up for me. – Locke Jun 25 '14 at 5:35
• An added note, since the wiki article does not mention it: one can look at ∈ meaning 'is' through the prism of sets representing the common property held by all its elements. e.g. Even = {0,2,4,..} and 'a ∈ Even' can be read as 'a is Even' – Henry Henrinson Jun 25 '14 at 11:37

$\in$ means "Element of".

For example, $a$ $\in$ A means Element of: $a$ is in A.

A numeric example would be: $\color{red}3 \in \{1, 2, \color{red}3, 4, 5\}$.

(mathematics) means that it is an element in the set of… For eg...x ∈ ℕ denotes that x is within the set of natural numbers.

The relation "is an element of", also called set membership, is denoted by the symbol "∈". Writing {\displaystyle x\in A} x\in A means that "x is an element of A". Equivalent expressions are "x is a member of A", "x belongs to A", "x is in A" and "x lies in A". The expressions "A includes x" and "A contains x" are also used to mean set membership, however some authors use them to mean instead "x is a subset of A".

Another possible notation for the same relation is {\displaystyle A\ni x,} A\ni x, meaning "A contains x", though it is used less often. The negation of set membership is denoted by the symbol "∉". Writing {\displaystyle x\notin A} x\notin A means that "x is not an element of A".

It means "in," as in "an element $e$ is in a set $S$." It's much quicker to write "$e \in S$." Long before text messaging, mathematicians were abbreviating things as much as they possibly could. Of course sets can be elements of others sets.

Certain conventions are often implied, so in some cases you might not see things like "$n \in \mathbb{Z}$" or "$x \in \mathbb{R}$" because it's understood.

• $\Bbb Z\in\Bbb Q$ and $\Bbb R\in \Bbb C$ are dead wrong, so I seriously doubt that anyone will see them, as you claim they will. Where would someone see this? Do you have a citation? – MJD Jun 27 '14 at 16:35
• @MJD "Dead wrong"? I don't feel like arguing about this, so I'm just removing that line. I shouldn't be surprised by this, given how y'all like to mark as off-topic questions that are clearly on-topic. – Robert Soupe Jun 27 '14 at 17:10
• One typically has $\mathbf{R}\subset\mathbf{C}$ and $\mathbf{Z}\subset\mathbf{Q}$, where $\subset$ denotes "is a subset of". – Gahawar Jun 27 '14 at 17:22
• Mathematicians have understood the distinction between $X\in Y$ and $X\subset Y$ since the time of Frege, in the late 19th century. Apparently you didn't get the memo. – MJD Jun 27 '14 at 17:24
• @MJD Nope, I didn't get that memo. I also didn't get the memo about how you have to treat people with extreme condescension for the tiniest inaccuracy. – Robert Soupe Jun 27 '14 at 17:41