Editing Mathematical notation (section)

== Symbols and typeface ==
{{Main|Glossary of mathematical symbols}}

The use of many symbols is the basis of mathematical notation. They play a similar role as words in [[natural language]]s. They may play different roles in mathematical notation similarly as verbs, adjective and nouns play different roles in a sentence.

=== Letters as symbols===
{{main|List of letters used in mathematics, science, and engineering}}

Letters are typically used for naming—in [[list of mathematical jargon|mathematical jargon]], one says ''representing''—[[mathematical object]]s. The [[Latin alphabet|Latin]] and [[Greek alphabet|Greek]] alphabets are used extensively, but a few letters of other alphabets are also used sporadically, such as the [[Hebrew alphabet|Hebrew]] {{tmath|\aleph}}, [[Cyrillic script|Cyrillic]] {{math|Ш}}, and [[Hiragana]] {{math|よ}}. Uppercase and lowercase letters are considered as different symbols. For Latin alphabet, different typefaces also provide different symbols. For example, <math>r, R, \R, \mathcal R, \mathfrak r,</math> and <math>\mathfrak R</math> could theoretically appear in the same mathematical text with six different meanings. Normally, roman upright typeface is not used for symbols, except for symbols representing a standard function, such as the symbol "<math>\sin</math>" of the [[sine function]].<ref>ISO 80000-2:2019</ref>

In order to have more symbols, and for allowing related mathematical objects to be represented by related symbols, [[diacritic]]s, [[subscript]]s and [[superscript]]s are often used. For example, <math>\hat {f'_1}</math> may denote the [[Fourier transform]] of the [[derivative]] of a [[function (mathematics)|function]] called <math>f_1.</math>

=== Other symbols ===
Symbols are not only used for naming mathematical objects. They can be used for [[operation (mathematics)|operation]]s <math>(+, -, /, \oplus, \ldots),</math> for [[relation (mathematics)|relation]]s <math>(=, <, \le, \sim, \equiv, \ldots),</math> for [[logical connective]]s <math>(\implies, \land, \lor, \ldots),</math> for [[quantifier (logic)|quantifier]]s <math>(\forall, \exists),</math> and for other purposes.

Some symbols are similar to Latin or Greek letters, some are obtained by deforming letters, some are traditional [[typographic symbol]]s, but many have been specially designed for mathematics.

=== International standard mathematical notation ===
The [[International Organization for Standardization]] (ISO) is an [[international standard]] development organization composed of representatives from the national [[Standards organization|standards organizations]] of member countries. The international standard [[ISO 80000-2]] (previously, [[ISO 31-11]]) specifies symbols for use in mathematical equations. The standard requires use of italic fonts for variables (e.g., {{nowrap|1=''E'' = ''mc''<sup>2</sup>}}) and roman (upright) fonts for mathematical constants (e.g., e or π).