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Lucas numbers have L 1 = 1, L 2 = 3, and L n = L n−1 + L n−2. Primefree sequences use the Fibonacci recursion with other starting points to generate sequences in which all numbers are composite. Letting a number be a linear function (other than the sum) of the 2 preceding numbers. The Pell numbers have P n = 2P n−1 + P n−2.
[2] [3] Historically, the concept of a proof and its associated mathematical rigour first appeared in Greek mathematics , most notably in Euclid 's Elements . [ 4 ] Since its beginning, mathematics was primarily divided into geometry and arithmetic (the manipulation of natural numbers and fractions ), until the 16th and 17th centuries, when ...
Mathematicians have noted tendencies in which definition is used, such as algebra texts including 0, [22] [d] number theory and analysis texts excluding 0, [22] [29] [30] logic and set theory texts including 0, [31] [32] [33] dictionaries excluding 0, [22] [34] school books (through high-school level) excluding 0, and upper-division college ...
Sugiharto was born in Medan, North Sumatra, Indonesia, on 29 April 1955. [3] Although his family originated in Java , they were living in Sumatra due to the Transmigrasi policy. [ 4 ] After doing an undergraduate degree at the University of Indonesia , he did a Master of Business Administration at the University of Amsterdam , graduating in ...
For some other divergent geometric series, including Grandi's series with ratio −1, and the series 1 + 2 + 4 + 8 + ⋯ with ratio 2, one can use the general solution for the sum of a geometric series with base 1 and ratio , obtaining , but this summation method fails for 1 + 1 + 1 + 1 + ⋯, producing a division by zero.
[1] [2] Data may represent abstract ideas or concrete measurements. [3] Data are commonly used in scientific research , economics , and virtually every other form of human organizational activity. Examples of data sets include price indices (such as the consumer price index ), unemployment rates , literacy rates, and census data.
The Battle of Semarang (Indonesian: Pertempuran Semarang), in Indonesia also known as Pertempuran Lima Hari (Five Days' Battle) [8] was a clash between Japanese forces of the Sixteenth Army and Indonesian forces consisting of People's Security Agency personnel and pemuda in October 1945 at the city of Semarang, Central Java. The battle is ...
[7] After no longer becoming minister, Bambang Brodjonegoro established his own executive office to manage his post-ministerial activities and disseminate his works and thoughts around May 2021. He returned to academia and became head of the Council of Professors of Faculty of Economy and Business University of Indonesia shortly after that. [ 8 ]