therefore sign

The therefore sign” is used especially in handwritten mathematical text as a shorthand of the or relationsMathworldPlanetmath:


It expresses that S2 has been inferred from S1 or from S1 and some preceding facts. The sign is rather a punctuation mark than a symbol of logical implication. Grammatically, it could be characterised a conclusive coordinating . The usage of the symbol is not mathematically well-defined, and it often means ‘we can conclude in context’ or ‘we can conclude from statements already shown or assumed to be true’.

For example, in determining an angle of a right triangleMathworldPlanetmath, one may write


Here, “” does not a proper implicationMathworldPlanetmath”, since the exact implication here would be


To obtain a strict implication, we would need to introduce some of the context. For instance, we know that, since α is an angle of a right triangle, 0α90, so what we wrote could be interpreted as the implication

sinα=12 0α90α=30.
Title therefore sign
Canonical name ThereforeSign
Date of creation 2013-03-22 17:55:51
Last modified on 2013-03-22 17:55:51
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 8
Author pahio (2872)
Entry type Definition
Classification msc 00A06
Classification msc 00A05
Related topic RingsOfRationalNumbers
Related topic LogarithmicScale