Information: - A mathematician is someone who uses an extensive knowledge of mathematics in his/her work, typically to solve mathematical problems. - A definition is a statement of the meaning of a term (a word, phrase, or other set of symbols). Definitions can be classified into two large categories, intensional definitions (which try to give the essence of a term) and extensional definitions (which proceed by listing the objects that a term describes). Another important category of definitions is the class of ostensive definitions, which convey the meaning of a term by pointing out examples. A term may have many different senses and multiple meanings, and thus require multiple definitions. - In complex analysis, an elliptic function is a meromorphic function that is periodic in two directions. Just as a periodic function of a real variable is defined by its values on an interval, an elliptic function is determined by its values on a fundamental parallelogram, which then repeat in a lattice. Such a doubly periodic function cannot be holomorphic, as it would then be a bounded entire function, and by Liouville's theorem every such function must be constant. In fact, an elliptic function must have at least two poles (counting multiplicity) in a fundamental parallelogram, as it is easy to show using the periodicity that a contour integral around its boundary must vanish, implying that the residues of all simple poles must cancel. - Mathematics (from Greek "mathma", knowledge, study, learning) is the study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics. - Niels Henrik Abel (5 August 1802 6 April 1829) was a Norwegian mathematician who made pioneering contributions in a variety of fields. His most famous single result is the first complete proof demonstrating the impossibility of solving the general quintic equation in radicals. This question was one of the outstanding open problems of his day, and had been unresolved for 250 years. He was also an innovator in the field of elliptic functions, discoverer of Abelian functions. Despite his achievements, Abel was largely unrecognized during his lifetime; he made his discoveries while living in poverty and died at the age of 26. - In mathematics , Abel 's inequality , named after Niels Henrik Abel , supplies a simple bound on the absolute value of the inner product of two vectors in an important special case . Let ( a1 , a2 , ... ) be a sequence of real numbers that is either nonincreasing or nondecreasing , and let ( b1 , b2 , ... ) be a sequence of real or complex numbers . If ( an ) is nondecreasing , it holds that - Quantity is a property that can exist as a magnitude or multitude. Quantities can be compared in terms of "more", "less", or "equal", or by assigning a numerical value in terms of a unit of measurement. Quantity is among the basic classes of things along with quality, substance, change, and relation. Some quantities are such by their inner nature (as number), while others are functioning as states (properties, dimensions, attributes) of things such as heavy and light, long and short, broad and narrow, small and great, or much and little. A small quantity is sometimes referred to as a quantulum. - Space is the boundless three-dimensional extent in which objects and events have relative position and direction. Physical space is often conceived in three linear dimensions, although modern physicists usually consider it, with time, to be part of a boundless four-dimensional continuum known as spacetime. The concept of space is considered to be of fundamental importance to an understanding of the physical universe. However, disagreement continues between philosophers over whether it is itself an entity, a relationship between entities, or part of a conceptual framework. 'abel's inequality' is related to which object entity through the relation of 'instance of'? Choices: - april - august - class - complex - constant - definition - elliptic function - entire function - equation - field - framework - function - integral - interval - mathematics - measurement - part - phrase - property - quantity - range - relation - relationship - result - single - space - statement - study - theorem - three - time - understanding - unit of measurement - variable - variety - work
theorem
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Information: - Bishkek (and ] respectively), formerly Pishpek and Frunze, is the capital and largest city of the Kyrgyz Republic. Bishkek is also the administrative center of the Chuy Region. The province surrounds the city, although the city itself is not part of the province, but rather a province-level unit of Kyrgyzstan. - Chuy Region or Chui Region (Kyrgyz: , "Cuy oblusu" ) is the northernmost region ("oblast") of the Kyrgyz Republic. It is bounded on the north by Kazakhstan, and clockwise, Issyk Kul Region, Naryn Region, Jalal-Abad Region and Talas Region. Its administrative center is Bishkek, but from 2003 to May 2006 it was Tokmok. - Kyrgyzstan (; "Kyrgyzstan"), officially the Kyrgyz Republic ("Krgz Respublikas"; "Kyrgyzskaya Respublika"), formerly known as Kirghizia, is a country in Central Asia. Landlocked and mountainous, Kyrgyzstan is bordered by Kazakhstan to the north, Uzbekistan to the west and southwest, Tajikistan to the southwest and China to the east. Its capital and largest city is Bishkek. - Lebedinovka ( Russian : ) is a village on the outskirts of the Kyrgyz capital Bishkek . Administratively , however , it is not part of the city , but is the center of the Alamudun District of Chuy Province , which surrounds Bishkek . Lebedinovka was established in 1898 . Its population is 20,709 , according to the census of 2009 . 'lebedinovka' is related to which object entity through the relation of 'country'? Choices: - kazakhstan - kyrgyzstan - uzbekistan
kyrgyzstan
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