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The Encyclopedia of Mathematics [7] defines interval (without a qualifier) to exclude both endpoints (i.e., open interval) and segment to include both endpoints (i.e., closed interval), while Rudin's Principles of Mathematical Analysis [8] calls sets of the form [a, b] intervals and sets of the form (a, b) segments throughout.
Beyond elementary mathematics, [] are mostly used for other purposes, e.g. to denote a closed interval, or an equivalence class, so they appear rarely for grouping. The usage of the word "brackets" varies from country. In the United States, the term denotes [], known elsewhere as "square brackets".
The following table lists many specialized symbols commonly used in modern mathematics, ordered by their introduction date. The table can also be ordered alphabetically by clicking on the relevant header title.
Glossary of mathematical symbols; List of logic symbols; Greek letters used in mathematics, science, and engineering; List of letters used in mathematics and science; List of mathematical uses of Latin letters; Unicode subscripts and superscripts; Unicode symbols; CJK Compatibility Unicode symbols includes symbols for SI units
The second is a link to the article that details that symbol, using its Unicode standard name or common alias. (Holding the mouse pointer on the hyperlink will pop up a summary of the symbol's function.); The third gives symbols listed elsewhere in the table that are similar to it in meaning or appearance, or that may be confused with it;
√ (square-root symbol) Denotes square root and is read as the square root of. Rarely used in modern mathematics without a horizontal bar delimiting the width of its argument (see the next item). For example, √2. √ (radical symbol) 1. Denotes square root and is read as the square root of.
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The main objective of interval arithmetic is to provide a simple way of calculating upper and lower bounds of a function's range in one or more variables. These endpoints are not necessarily the true supremum or infimum of a range since the precise calculation of those values can be difficult or impossible; the bounds only need to contain the function's range as a subset.