Therefore sign (∴)
The therefore sign (∴), three dots in a triangle with one on top, means “therefore”. It comes before a conclusion that follows from the lines above it.
How to read it
It is read “therefore”, and Unicode names it THEREFORE (U+2234). Its partner, with one dot below and two above, is the because sign ∵ (U+2235). Cajori’s history (1929) describes ∴ as widely used in English and American books.
Also searched as: ∴, therefore symbol.
∴ or ∵
The two were once used interchangeably. Cajori found that through the eighteenth century ∵ was used for “therefore” about as often as ∴. Using ∵ for “because” began in Britain and the United States in the nineteenth century, and it did not become as common as ∴ for “therefore”.
Differences by country
Cajori wrote that both signs were very rare in mathematical publications on the European Continent, except in papers on symbolic logic.
Look-alikes
Unicode cross-refers ∴ to ⛬ (U+26EC), HISTORIC SITE, one of the map symbols Unicode took from the ARIB STD B24 standard.
More math symbols
Browse symbols drawn with triangles.
Sources
- Mathematical Operators: Range 2200–22FF (code chart), The Unicode Standard, Version 18.0, Unicode Consortium, Mathematical Operators, 2234–2235
- Miscellaneous Symbols, Range: 2600–26FF (code chart), The Unicode Standard, Unicode Consortium, Miscellaneous Symbols, 26EC
- Earliest Uses of Symbols of Set Theory and Logic, Jeff Miller, Earliest Uses of Various Mathematical Symbols, MacTutor History of Mathematics, University of St Andrews, Therefore and because
- A History of Mathematical Notations, Vol. II: Notations Mainly in Higher Mathematics, Florian Cajori (Chicago: Open Court, 1929); full text of the Wellcome Collection copy, Internet Archive, §§ 667–669, pp. 282–283
Last reviewed September 30, 2026 by Rory Hansen. How we research