Definition:Parenthesis
Definition
Parenthesis is the operation of encompassing a compound substatement of a given compound statement such that it is treated as a single entity. Such a statement is referred to as being in parenthesis.
Brackets are used to identify the substatements of a compound statement that are in parenthesis.
The brackets that are usually used are round ones:
- $\left({\textrm {This} \ \textrm {statement} \ \textrm {is} \ \textrm {in} \ \textrm {parenthesis}}\right)$
Differently shaped brackets are used in different contexts. In the context of a (logical) statement, they are sometimes referred to as parentheses (the plural of the word parenthesis, which is of Greek origin).
There is no universal convention as to exactly what shaped brackets are used for parentheses, but (usually) round brackets "$\left({\;}\right)$" are used. The elegantly-presented Keisler and Robbin
An obvious definition: "$($" is a left bracket, while "$)$" is a right bracket.
Some authors, when writing complicated statements with nested parentheses, use differently shaped brackets for each different parenthesis, in an attempt to make it clearer which brackets go with which substatements. However, some have the opinion that this does not actually aid comprehension and can add unnecessary confusion - especially when particular bracket styles are being used for particular mathematical tasks, as they frequently are.
It also happens, unfortunately, that square brackets do not render well in all browsers when they have been automatically scaled by our rendering software.
Therefore it is recommended that on ProofWiki round brackets are used throughout for parenthesis.
Notes
Sources
- Paul R. Halmos: Naive Set Theory (1960)... (previous)... (next): $\S 2$: The Axiom of Specification
- E.J. Lemmon: Beginning Logic (1965): $\S 1.2$ Implicit: "(we introduce brackets here in an entirely obvious way)".
- D.J. O'Connor and Betty Powell: Elementary Logic (1980): $\S 1.5$
