What gifts did the Martians bring back to their homeland?

during the Christmas season, the American commodity market was a sale and a lot of bargains. What good did the Martians bring back?

AMonth -Day, on Christmas Day, the Martians were visitingJ.keiskerprofessor, the problem of linear motion of particles is discussed in detail. In other words, pointxmoving in a straight line, infinitely close to the pointa, Arrival pointa, and then leave the pointa. The problem seems simple, but it's not.

1975years7month, the translation of "Marx's Mathematical Manuscript" was published in a language that was proud of being faithful to Marx's original text, which lacked many prepositions (for example, of, for, fromand so on), the Chinese translator dare not add up, make the Chinese reader difficult to read, its "history file" shelved. 1983at the death of Marx -during the anniversary celebration, theThe New Park"published the English version of Marx's mathematical manuscript, addingAndy Blundenexplanatory article, so that the vast number of readers to learn the "Marx Mathematical manuscript" interest greatly increased.

Marx's contribution to mathematics does not lie in increasing the proofs of mathematical theorems, but in introducing the viewpoint of materialist dialectics into mathematics. It's a great thing. What is dialectics (dialectics)? In the ancient Greek era, the so-called "dialectical" refers to the opposing sides through the "dialogue" to persuade each other's "debate technique." In modern times, Hegel promoted it to the concept of "development of Things" (under the premise of Idealism), and Marx introduced dialectics into historical materialism.

taking the linear motion of a particle as an example, Marx argues that when a particlexunrestricted access to fixed pointsawhen, at some point, a particlex, both at the pointa(coincident with), not pointa(away from the pointa). How should we understand this phenomenon? Only the introduction of "dialectical thinking" in mathematics can reasonably explain this paradox phenomenon.

fromJ.keislerprofessor's infinitesimal analysis point of view, when the particlexinfinitely close to the fixed pointawhen the particlexthe standard partSt (x) =a(coincident with), at which point the particlexstill in motion. However, when the particlexover the fixed pointathen move on, and the particlexis no longer equal to the fixed pointaup. In the view of Dialectics, that is, from the perspective of infinitesimal analysis, continuous motion presents some discontinuity.

            Mars people visit j Keisler Professor brings back the present is in mathematics dialectical thinking mode, said to understand is: "Marx Mathematics manuscript" English translation!

Description: During New Year's Day, I suggest you flip through Andy Blunden the article: Marx ' s Brilliant Study of Mathematics . This article is of great reading value.

What gifts did the Martians bring back to their homeland?