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Examples of unexpected applications of mathematical theories can be found in many areas of mathematics. A notable example is the prime factorization of natural numbers that was discovered more than 2,000 years before its common use for secure internet communications through the RSA cryptosystem. [127]
For example, the integers are made by adding 0 and negative numbers. The rational numbers add fractions, and the real numbers add infinite decimals. Complex numbers add the square root of −1. This chain of extensions canonically embeds the natural numbers in the other number systems. [6] [7] Natural numbers are studied in different areas of math.
Algebra is the branch of mathematics that studies certain abstract systems, known as algebraic structures, and the manipulation of expressions within those systems. It is a generalization of arithmetic that introduces variables and algebraic operations other than the standard arithmetic operations, such as addition and multiplication.
Divide and conquer divides the problem into multiple subproblems and so the conquer stage is more complex than decrease and conquer algorithms. [citation needed] An example of a decrease and conquer algorithm is the binary search algorithm. Search and enumeration Many problems (such as playing chess) can be modelled as problems on graphs.
All these sequences may be viewed as generalizations of the Fibonacci sequence. In particular, Binet's formula may be generalized to any sequence that is a solution of a homogeneous linear difference equation with constant coefficients. Some specific examples that are close, in some sense, to the Fibonacci sequence include:
In probability theory, the expected value (also called expectation, expectancy, expectation operator, mathematical expectation, mean, expectation value, or first moment) is a generalization of the weighted average.
The English name of "Singapore" is an anglicisation of the native Malay name for the country, Singapura (pronounced), which was in turn derived from the Sanskrit word for 'lion city' (Sanskrit: सिंहपुर; romanised: Siṃhapura; Brahmi: 𑀲𑀺𑀁𑀳𑀧𑀼𑀭; literally "lion city"; siṃha means 'lion', pura means 'city' or 'fortress'). [9]
41.6 2017 41.59 2017 Denmark: Northern Europe: High income 28.3 2021 28.47 2022 Dominican Republic: Caribbean: Upper middle income 37.0 2022 38.10 2022 Algeria: Northern Africa: Upper middle income 27.6 2011 27.62 2012 Ecuador: South America: Upper middle income 44.6 2023 45.47 2022 Egypt: Northern Africa: Lower middle income 31.9
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