Rightwards arrow with tail

In Z notation, ↣ marks a total injection: every input gets one output, and distinct inputs get distinct outputs. Its tail signals the one-to-one rule.

Text symbol

What ↣ means

A history of mathematical symbols records Bourbaki, a group of mathematicians, using arrows between elements by 1939; broader map notation appears around 1940.

In Z notation, ↣ maps every set member to exactly one member of another set, with no shared outputs. A plain arrow lacks this condition.

The MathML operator dictionary—the webpage math-layout rules—marks ↣ as stretchy, so it may widen to fit an expression.

Part of the collection

➡️

Arrow Symbols

Don't confuse it with

↦

Rightwards Arrow From Bar

↣ versus maplet ↦: a maplet assigns one value to an argument; ↣ marks a total injection between sets.

⤔

Rightwards Arrow With Tail With Vertical Stroke

⤔ adds a vertical stroke. In Z notation it marks a partial injection, while ↣ marks a total one.

↪

Left Arrow Curving Right

The hooked arrow ↪ usually marks an inclusion or embedding. ↣ marks an injection or monomorphism.

↠

Rightwards Two Headed Arrow

↠ has two heads and marks a surjection. The tail on ↣ marks an injection.

Combination ideas

A total injection from set X to set Y.

The natural numbers map one-to-one into the integers.

The tailed arrow pair, pointing both ways.

Questions people ask

Why does ↣ show as a box on some devices?

Because that device's fonts have no glyph for it. The character is still correct and still copies correctly — the box is a missing glyph, not a broken character.