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Pythagoras with a tablet of ratios, detail from The School of Athens by Raphael (1509) Greek mathematics allegedly began with Thales of Miletus (c. 624–548 BC). Very little is known about his life, although it is generally agreed that he was one of the Seven Wise Men of Greece.
In a vector space, the additive inverse −v (often called the opposite vector of v) has the same magnitude as v and but the opposite direction. [11] In modular arithmetic, the modular additive inverse of x is the number a such that a + x ≡ 0 (mod n) and always exists. For example, the inverse of 3 modulo 11 is 8, as 3 + 8 ≡ 0 (mod 11). [12]
Roger Apéry (1916–1994) - Professor of mathematics and mechanics at the University of Caen Proved the irrationality of zeta(3). [11] Tom M. Apostol (1923–2016) - Professor of mathematics in California Institute of Technology, [12] he has authored a number of books about mathematics.
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On the other hand, the completions with respect to the other non-trivial absolute values give the fields of p-adic numbers, where is a prime integer number (see below); since the -adic absolute values satisfy the ultrametric property, then the -adic number fields are non-Archimedean as normed fields (they cannot be made into ordered fields).
Any involution is a bijection.. The identity map is a trivial example of an involution. Examples of nontrivial involutions include negation (x ↦ −x), reciprocation (x ↦ 1/x), and complex conjugation (z ↦ z) in arithmetic; reflection, half-turn rotation, and circle inversion in geometry; complementation in set theory; and reciprocal ciphers such as the ROT13 transformation and the ...
P ' is the inverse of P with respect to the circle. To invert a number in arithmetic usually means to take its reciprocal. A closely related idea in geometry is that of "inverting" a point. In the plane, the inverse of a point P with respect to a reference circle (Ø) with center O and radius r is a point P ', lying on the ray from O through P ...
Diophantus was born into a Greek family and is known to have lived in Alexandria, Egypt, during the Roman era, between AD 200 and 214 to 284 or 298. [6] [11] [12] [a] Much of our knowledge of the life of Diophantus is derived from a 5th-century Greek anthology of number games and puzzles created by Metrodorus.