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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
The R40 numbers 3.00 and 6.00 are higher than they "should" be by interpolation, in order to give rounder numbers. In some applications more rounded values are desirable, either because the numbers from the normal series would imply an unrealistically high accuracy, or because an integer value is needed (e.g., the number of teeth in a gear).
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.
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.
WPTA (channel 21) is a television station in Fort Wayne, Indiana, United States, affiliated with ABC, NBC, and MyNetworkTV.It is owned by Gray Television alongside CW+ affiliate WISE-TV (channel 33).
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Below is a sortable list of countries by number of Internet users as of 2024. Internet users are defined as persons who accessed the Internet in the last 12 months from any device, including mobile phones. [Note 1] Percentage is the percentage of a country's population that are Internet users. Estimates are derived either from household surveys ...