Fixed point (mathematics)hatnote|1=Fixed points in mathematics are not to be confused with other uses of "fixed point", or stationary points where math|1=f(x) = 0. In mathematics, a fixed point (sometimes shortened to fixpoint), also known as an invariant point, is a value that does not change under a given transformation. Specifically for functions, a fixed point is an element that is mapped to itself by the function. Formally, c is a fixed point of a function f if c belongs to both the domain and the codomain of f, and f(c) = c.
Cyrillic alphabetsNumerous Cyrillic alphabets are based on the Cyrillic script. The early Cyrillic alphabet was developed in the 9th century AD and replaced the earlier Glagolitic script developed by the Byzantine theologians Cyril and Methodius. It is the basis of alphabets used in various languages, past and present, Slavic origin, and non-Slavic languages influenced by Russian. As of 2011, around 252 million people in Eurasia use it as the official alphabet for their national languages. About half of them are in Russia.
Bulgarian languageBulgarian (bʌlˈɡɛəriən, bʊlˈ- ; bǎlgarski, ˈbɤɫɡɐrski) is an Eastern South Slavic language spoken in Southeast Europe, primarily in Bulgaria. It is the language of the Bulgarians. Along with the closely related Macedonian language (collectively forming the East South Slavic languages), it is a member of the Balkan sprachbund and South Slavic dialect continuum of the Indo-European language family.
