What does the symbol $\in$ mean?

Question

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:

Answer 1

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.

Answer 2

$\in$ 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.