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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.
A repeating decimal or recurring decimal is a decimal representation of a number whose digits are eventually periodic (that is, after some place, the same sequence of digits is repeated forever); if this sequence consists only of zeros (that is if there is only a finite number of nonzero digits), the decimal is said to be terminating, and is not considered as repeating.
In modern set-theoretic mathematics, a more abstract construction [35] [36] allowing one to define arithmetical operations without any case distinction is often used instead. [37] The integers can thus be formally constructed as the equivalence classes of ordered pairs of natural numbers ( a , b ) .
Studying topological features such as these led to the notion of the cycles that represent homology classes (the elements of homology groups). For example, the two embedded circles in a figure-eight shape provide examples of one-dimensional cycles, or 1-cycles, and the 2-torus T 2 {\displaystyle T^{2}} and 2-sphere S 2 {\displaystyle S^{2 ...
Flowchart of using successive subtractions to find the greatest common divisor of number r and s. In mathematics and computer science, an algorithm (/ ˈ æ l ɡ ə r ɪ ð əm / ⓘ) is a finite sequence of mathematically rigorous instructions, typically used to solve a class of specific problems or to perform a computation. [1]
The history of mathematics deals with the origin of discoveries in mathematics and the mathematical methods and notation of the past.Before the modern age and the worldwide spread of knowledge, written examples of new mathematical developments have come to light only in a few locales.
The number π (/ p aɪ / ⓘ; spelled out as "pi") is a mathematical constant, approximately equal to 3.14159, that is the ratio of a circle's circumference to its diameter.It appears in many formulae across mathematics and physics, and some of these formulae are commonly used for defining π, to avoid relying on the definition of the length of a curve.
[11] [12] While the reliability of Wikipedia was frequently criticized in the 2000s, it has improved over time, receiving greater praise from the late 2010s onward [3] [13] [14] while becoming an important fact-checking site. [15] [16] Articles on breaking news are often accessed as sources for frequently updated information about those events ...
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