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Two arrows distinguished by a short bar at the tail, one relating sets and the other relating an element to its image.
A plain arrow relates *sets*: it declares a function's domain and codomain. A barred arrow relates *elements*: it says where one particular input goes. So a function is declared with a plain arrow and its rule is given with a barred one, and using the plain arrow for both — the commonest error in written mathematics — states that a number is a set. The bar at the tail is the only visible difference.
One relates sets, the other relates an element to its image.
| Function arrow | Maps-to arrow | |
|---|---|---|
| Tail | Plain. | Crossed by a short upright bar. |
| What sits either side | Sets — the domain and the codomain. | Elements — an input and its image. |
| Read aloud as | “from … to …” | “maps to” |
| Relationship (from Symbolwise's records) | Commonly confused with Maps-to arrow — One relates sets, the other relates an element to its image. | Commonly confused with Function arrow — One says what happens to an element, the other which sets are involved. |
ISO 80000-2:2019, Quantities and units — Part 2: Mathematics
International Organization for Standardization · retrieved 2026-07-31
Paywalled and NOT READ for this batch. Registered so the standard can be named as existing and as covering mathematical signs; it supports no meaning in any record. See docs/paywalled-standards.md.
Unicode Code Chart: Mathematical Operators (U+2200–U+22FF)
The Unicode Consortium · retrieved 2026-07-30
Authoritative for the character's code point, name and block only. Unicode assigns identity; it does not define what a symbol means in use.
AMS Style Guide — mathematical notation
American Mathematical Society · retrieved 2026-08-22
A publisher's house style rather than a standard. Authoritative about how notation is set in mathematical publishing; it does not decide what a symbol means.
Alpha is a Greek letter and stands for a quantity — an angle, a coefficient, a significance level. The proportionality sign is an operator and stands between two quantities to say they keep a constant ratio. The drawings differ in that the proportionality sign's right-hand stroke runs out in an open curve rather than closing into the letter's tail.
Look at the left-hand edge. A straight flat back is an AND gate: the output is true only when every input is. A curved concave back is an OR gate: true when any input is. Everything else about the shapes is similar, which is why the back edge is worth checking deliberately rather than at a glance.
Look at what follows. A prefix never stands alone — it is glued to a unit symbol, as in kW or kg. A constant stands by itself in an equation. Careful physical writing subscripts the constant as k_B for exactly this reason, and the kelvin's capital K is a third claimant to the same letter.
Length is the tell. A crescendo hairpin is drawn long, below a stave, and spans the passage it applies to — its extent *is* the instruction. A less-than sign is one character wide and sits between two values. If it stretches, it is music; if it fits between two numbers, it is mathematics.