Therefore sign
From Wikipedia, the free encyclopedia
|
∴
|
|---|
|
apostrophe ( ’ ' ) |
| Interword separation |
|
spaces ( ) ( ) ( ) |
| General typography |
|
ampersand ( & ) |
| Uncommon typography |
|
asterism ( ⁂ ) |
In a mathematical proof, the therefore sign (∴) is a symbol that is sometimes placed before a logical consequence, such as the conclusion of a syllogism. The symbol consists of three dots placed in a triangle. In reading, it is pronounced Therefore, …. It is Unicode character U+2234. While it is not generally used in formal work, it is often used in mathematics and shorthand.
Contents |
[edit] History
According to Cajori, A History of Mathematical Notations, the therefore sign was first used by Johann Rahn in 1659, in the original German edition of his book Teutsche Algebra.
[edit] Related signs
The inverted form ∵, known as the because sign, is sometimes used as a shorthand form of "because". This is Unicode character U+2235.
The therefore sign is sometimes used as a substitute for an asterism [⁂].
To denote logical implication or entailment, various signs are used in mathematical logic: →, ⇒, ⊃, ⊢, ⊨. These symbols are then part of a mathematical formula, and are not considered to be punctuation. In contrast, the therefore sign is traditionally used as a punctuation mark, and does not form part of a formula.
[edit] Examples
Used in a syllogism:
- All humans are mortal.
- Socrates is a human.
- ∴ Socrates is mortal.
