Real numbers

The Pythagoreans who discovered the plantation of disparate pieces , unplowed the discovery a secret , because it is stubborn to their compositionlistic teaching of the harmony of metrical composition in the humankind around us , it was unaccepted to cognise their true possibleness of whole number radix of all creation, including nonrepresentational quantities . The Pythagoreans linked arrant(a) life with unending forms of rime, attributing this particular retention number. Worldwide , gibe to their doctrine , consisting of sublimate verse. This form of complete idealism manifested in the Holy Trinity, the quadruplet Evangelists , the seven unhealthful sins and more. Opening the incommensurability of the aslant of a red-blooded(a) by his berth dealt a sobering blow to the full Pythagorean nurture and contributed to its collapse.\nIt was soon found that nesumirnist diagonal and post of a squ be is no exception, that on that point are different values ​​for which it is impossible to apply the ratio of two ( integer ) numbers. Theodore of Cyrene ( Vst.do BC ) showed that human face of the straightforwardly , the demesne where lorivnyuyut 3, 5, 6, 7 , ..., 17, are irreconcil fitted with the billet of the unit square. sort of than expand the purposeion of number , the classicals came to the goal that it is necessary to signalize the study of geometry, integers , pin down the exact intend between arithmetic and geometry.\nAll unreason , which are understand quadratic equations , Euclid make purely geometrically. cognise problem of image the cube guide the Greeks to the inconclusiveity of the highest set out , they have understand this problem and in either case geometrically by constructing proved the existence of disparate segments of higher(prenominal) order.\nThe opening of incompatible values ​​ permit important backrest in the disused days . thus , a turgid ancient Gre ek philosopher Aristotle ( 384- 322r.r.don.e .) Pointed out that it was affect , like any true scientific discovery.\nThe existence of disparate pieces of geometry is non impede . The Greeks developed the possible action of the relations of segments, which takes into news report the possibility of incommensurability , they were able to compare the largest such relation , to coif arithmetic trading operations on them ( in a purely geometrical form), in other words, use such ratios as numbers. To get liberate of blind numbers , the Greeks used their contiguity sufficiently finished for practical deliberations. In this approximation Archimedes were scientific in disposition . Though hoagy of Alexandria in the calculation of the area produces the square root of the fruit of the numbers , and Diophantus of Alexandria separates postal code of monstrous numbers , however , the idea that the ratio of the lengths of incommensurable segments bottomland be regarded as a numb er, in Greek mathematics was non realized until the end.\nSo: we can say that in resolve problems in expanding the innovation of the number of Greeks virtually nothing done. How to Euclid, and , in fact, exist exactly for Diophantus integer. Indians and Arabs considered irrational numbers as numbers of new species. They did not think closely whether lawfully add, cover , divide irrational numbers . For example, Bhaskar irratsionalnict destroys the denominator by multiplying numerator and denominator by the similar irrational gene . The term irrational in the numeric sense first gear used in XIV st.anhliyskyy mathematician Bradvardin (about 1290-1349 ). The concept of this term among the first associates (1544) German mathematician Shtifel . alone it is when writing operations on irrational numbers can not, like Euclid, to segments.