Right arrow (→) in LaTeX

Q: What is the difference between \to and \rightarrow?

None visually or semantically, \to is simply a shorter alias for \rightarrow, and both produce the identical → glyph. \to is more common in limits and inline text purely because it is quicker to type.

Q: What is the difference between \to and \mapsto?

\to connects a domain and codomain, as in f : A \to B, describing where a function's inputs and outputs live in general. \mapsto shows the specific rule applied to an individual element, as in x \mapsto x^2, showing exactly what happens to x.

Q: How do I write a limit with an arrow in LaTeX?

Use \lim_{x \to a} f(x), placing the variable and its target inside the subscript of \lim, connected by \to.

Q: How do I get a longer arrow?

Use \longrightarrow instead of \rightarrow; it produces a stretched-out version of the same arrow, useful for labelled arrows or commutative diagrams.

\rightarrow (or its alias \to) typesets a rightward arrow →, used for functions, limits, sequences and mappings.

\to

LaTeX command

\rightarrow

Not the symbol you meant? Draw it to find the command →

The rightward arrow shows up in several distinct mathematical roles. In function notation, f : $A \to B$ declares that f maps elements of A to elements of B. In limits, $x \to \infty$ or $n \to 0$ describes a variable approaching a value. In sequences and processes, it can show one state evolving into the next.

\to is simply a shorter alias for \rightarrow, producing an identical glyph; most authors use \to in running text and limits for brevity, and \rightarrow when spelling things out feels clearer, such as in a labelled diagram. Neither is more correct than the other.

For showing exactly where an element goes under a function, use \mapsto instead of \rightarrow: $x \mapsto x^{2}$ reads 'x maps to x squared', pairing naturally with the function declaration f : \mathbb{R} \to \mathbb{R},\ $x \mapsto x^{2}$ . Reserve \rightarrow for the domain-to-codomain statement and \mapsto for the specific rule.

Other forms

\toalias, common in limits

\leftarrowleft (←)

\leftrightarrowboth ways (↔)

\mapstomaps to (↦)

Examples

f : A \to B

$f : A \to B$

a function from A to B

x \mapsto x^{2}

$x \mapsto x^2$

the squaring map, paired with \mapsto not \to

x \to \infty lim \frac{1}{x} = 0

$\lim_{x \to \infty} \frac{1}{x} = 0$

x approaching infinity in a limit

n \to \infty

$n \to \infty$

a sequence index tending to infinity

f : R \to R, x \mapsto x^{2}

$f : \mathbb{R} \to \mathbb{R}, \quad x \mapsto x^2$

a full function declaration combining \to and \mapsto

Tips and common mistakes

Use \to (shorthand) or \rightarrow (full name) interchangeably, they produce the same arrow; pick one convention and keep it consistent within a document.
Use \rightarrow for the domain-to-codomain statement, f : $A \to B$ , and \mapsto for the explicit rule on elements, $x \mapsto f$ (x); mixing them up is a very common notational slip.
In limits, always attach the arrow to the variable and its target directly under \lim: \lim_{x \to a} f(x), not as separate floating symbols.
Do not use \rightarrow for logical implication, use \implies or \Rightarrow instead; the plain arrow is reserved for functions, limits and mappings in most conventions.
For a longer, more visually prominent arrow, for instance over a long label or in a commutative diagram, use \longrightarrow instead.

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FAQ

What is the difference between \to and \rightarrow?

None visually or semantically, \to is simply a shorter alias for \rightarrow, and both produce the identical → glyph. \to is more common in limits and inline text purely because it is quicker to type.

What is the difference between \to and \mapsto?

\to connects a domain and codomain, as in f : $A \to B$ , describing where a function's inputs and outputs live in general. \mapsto shows the specific rule applied to an individual element, as in $x \mapsto x^{2}$ , showing exactly what happens to x.

How do I write a limit with an arrow in LaTeX?

Use \lim_{x \to a} f(x), placing the variable and its target inside the subscript of \lim, connected by \to.

How do I get a longer arrow?

Use \longrightarrow instead of \rightarrow; it produces a stretched-out version of the same arrow, useful for labelled arrows or commutative diagrams.

Right arrow (→) in LaTeX

Other forms

Examples

Tips and common mistakes

Working from handwritten notes?

FAQ

See also