Syntactic monoidIn mathematics and computer science, the syntactic monoid of a formal language is the smallest monoid that recognizes the language . The free monoid on a given set is the monoid whose elements are all the strings of zero or more elements from that set, with string concatenation as the monoid operation and the empty string as the identity element. Given a subset of a free monoid , one may define sets that consist of formal left or right inverses of elements in .
SimulationA simulation is the imitation of the operation of a real-world process or system over time. Simulations require the use of models; the model represents the key characteristics or behaviors of the selected system or process, whereas the simulation represents the evolution of the model over time. Often, computers are used to execute the simulation. Simulation is used in many contexts, such as simulation of technology for performance tuning or optimizing, safety engineering, testing, training, education, and video games.
Definable real numberInformally, a definable real number is a real number that can be uniquely specified by its description. The description may be expressed as a construction or as a formula of a formal language. For example, the positive square root of 2, , can be defined as the unique positive solution to the equation , and it can be constructed with a compass and straightedge. Different choices of a formal language or its interpretation give rise to different notions of definability.
Languages of IndiaLanguages spoken in the Republic of India belong to several language families, the major ones being the Indo-Aryan languages spoken by 78.05% of Indians and the Dravidian languages spoken by 19.64% of Indians; both families together are sometimes known as Indic languages. Languages spoken by the remaining 2.31% of the population belong to the Austroasiatic, Sino–Tibetan, Tai–Kadai, and a few other minor language families and isolates. According to the People's Linguistic Survey of India, India has the second highest number of languages (780), after Papua New Guinea (840).
Indian classical danceIndian classical dance, or Shastriya Nritya, is an umbrella term for different regionally-specific Indian classical dance traditions, rooted in predominantly Hindu musical theatre performance, the theory and practice of which can be traced to the Sanskrit text Natya Shastra. The number of Indian classical dance styles ranges from eight to twelve, or more, depending on the source and scholar; the main organisation for Indian arts preservation, the Sangeet Natak Academy (as well as India’s Ministry of Culture), recognizes eight – Bharatanatyam, Kathak, Kuchipudi, Odissi, Kathakali, Sattriya, Manipuri and Mohiniyattam.
Hyperreal numberIn mathematics, the system of hyperreal numbers is a way of treating infinite and infinitesimal (infinitely small but non-zero) quantities. The hyperreals, or nonstandard reals, *R, are an extension of the real numbers R that contains numbers greater than anything of the form (for any finite number of terms). Such numbers are infinite, and their reciprocals are infinitesimals. The term "hyper-real" was introduced by Edwin Hewitt in 1948. The hyperreal numbers satisfy the transfer principle, a rigorous version of Leibniz's heuristic law of continuity.
Transcendental numberIn mathematics, a transcendental number is a real or complex number that is not algebraic – that is, not the root of a non-zero polynomial of finite degree with rational coefficients. The best known transcendental numbers are π and e. Though only a few classes of transcendental numbers are known – partly because it can be extremely difficult to show that a given number is transcendental – transcendental numbers are not rare: indeed, almost all real and complex numbers are transcendental, since the algebraic numbers form a countable set, while the set of real numbers and the set of complex numbers are both uncountable sets, and therefore larger than any countable set.
