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I am currently studying discrete mathematics, and I have very little background knowledge, and I was wondering what the symbol "$\in$" means.

The following is where I encountered this symbol:

Vector addition

Daniel W. Farlow
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Oliver K
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  • It means "an element of" . So, saying that, e.g. $x\in \mathbb R$ just means that "$x$ is an element of $\mathbb R$", i.e. $x$ is a real number. – lulu Aug 04 '15 at 02:14
  • $\mathbb R^2$, by the way, is the set of ordered pairs of reals — equivalently, it's the plane, or the set of points in the plane. (They're equivalent because of coordinates.) – Akiva Weinberger Aug 04 '15 at 02:51

2 Answers2

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The symbol $$ \Huge\in $$ means "in" and is actually typeset by \in to reflect this.

In general, if $A$ is any set (whose elements may be numbers or any other objects), we write $x\in A$ to indicate that $x$ is a member (or an element) of $A$. Now, if $x$ is not a member of $A$, then we write $x\not\in A$, and this is typeset by x\not\in A.

Daniel W. Farlow
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$\in$ means "is an element of", or more simply, "is in", which is why it is \in in LaTeX. For example:

  • "Let $x \in \mathbb{Z}$" = Let $x$ be an integer.

  • "Let $x \in \{0, 1\}$" = Let $x$ be either $0$ or $1$.

Note, that there is also the notation $\ni$, which means the same thing in the other order. For example, $x \in \mathbb{Z}$ is equivalent to $\mathbb{Z} \ni x$. This is read as "contains", and has LaTeX code \ni.

Caleb Stanford
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