Because sign (∵)
The because sign (∵) is three dots in a triangle, two on top and one below. It is read “because” and comes before a reason: ∵ x = 2, ∴ x² = 4 reads “because x is 2, x squared is 4”.
Easily confused with
How to read it
Unicode names it BECAUSE (U+2235), next to THEREFORE (U+2234) in its Mathematical Operators block. It is the therefore sign turned upside down: ∴ has one dot on top, ∵ has one dot below. Florian Cajori, in A History of Mathematical Notations (1929), found that ∵ for “because” did not become as widely accepted in Britain and America as ∴ for “therefore”.
Also searched as: ∵, because symbol.
∵ or ∴
The only difference is which way up the triangle is. ∴ (therefore), with one dot on top, comes before a conclusion; ∵ (because), with one dot at the bottom, comes before a reason. Cajori found both signs very rare in mathematical publications on the European Continent, except in papers on symbolic logic.
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
- 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 October 1, 2026 by Rory Hansen. How we research