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Hometherefore sign

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# therefore sign

The therefore sign “$\therefore$” is used especially in handwritten mathematical text as a shorthand of the word ‘therefore’ or ‘thus’, between some sentences or relations:

$S_{1}\quad\therefore\;S_{2}$ |

It expresses that $S_{2}$ has been inferred from $S_{1}$ or from $S_{1}$ 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 conjunction. 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 triangle, one may write

$\sin\alpha=\frac{1}{2}\quad\therefore\;\alpha=30^{\circ}$ |

Here, “$\therefore$” does not represent a proper implication “$\Rightarrow$”, since the exact implication here would be

$\sin\alpha=\frac{1}{2}\;\,\Leftarrow\;\,\alpha=30^{\circ}.$ |

To obtain a strict implication, we would need to introduce some of the context. For instance, we know that, since $\alpha$ is an angle of a right triangle, $0^{\circ}\leq\alpha\leq 90^{\circ}$, so what we wrote could be interpreted as the implication

$\sin\alpha=\frac{1}{2}\;\land\;0^{\circ}\leq\alpha\leq 90^{\circ}\;\,% \Rightarrow\;\,\alpha=30^{\circ}.$ |

## Mathematics Subject Classification

00A06*no label found*00A05

*no label found*

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