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The long real line pastes together ℵ 1 * + ℵ 1 copies of the real line plus a single point (here ℵ 1 * denotes the reversed ordering of ℵ 1) to create an ordered set that is "locally" identical to the real numbers, but somehow longer; for instance, there is an order-preserving embedding of ℵ 1 in the long real line but not in the real ...
Given real numbers x and y, integers m and n and the set of integers, floor and ceiling may be defined by the equations ⌊ ⌋ = {}, ⌈ ⌉ = {}. Since there is exactly one integer in a half-open interval of length one, for any real number x, there are unique integers m and n satisfying the equation
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
The classical objects of interest in arithmetic geometry are rational points: sets of solutions of a system of polynomial equations over number fields, finite fields, p-adic fields, or function fields, i.e. fields that are not algebraically closed excluding the real numbers.
The number 10,000 is used to express an even larger approximate number, as in Hebrew רבבה r e vâvâh, [36] rendered into Greek as μυριάδες, and to English myriad. [37] Similar usage is found in the East Asian 萬 or 万 (lit. 10,000; pinyin: wàn), and the South Asian lakh (lit. 100,000). [38]
It is still prevalent in projection systems, using anamorphic lenses, and supported by a number of consumer electronics devices, including Blu-ray players and video scalers. It is also used in computer monitors, where the term "21:9" can represent aspect ratios of 43:18 (2.3 8 :1 or 21.5:9) and 12:5 (2.4:1 or 21.6:9) in addition to 64:27.
The number e is a mathematical constant approximately equal to 2.71828 that is the base of the natural logarithm and exponential function.It is sometimes called Euler's number, after the Swiss mathematician Leonhard Euler, though this can invite confusion with Euler numbers, or with Euler's constant, a different constant typically denoted .
The following are some of the gene count estimates of human chromosome 2. Because researchers use different approaches to genome annotation their predictions of the number of genes on each chromosome vary. Among various projects, the collaborative consensus coding sequence project takes an extremely conservative strategy. So CCDS's gene number ...