A History of Greek Mathematics, Volume 2: From Aristarchus by Thomas Heath PDF

By Thomas Heath

ISBN-10: 0486240746

ISBN-13: 9780486240749

Volume 2 of an authoritative two-volume set that covers the necessities of arithmetic and contours each landmark innovation and every vital determine, including Euclid, Apollonius, and others.

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Additional resources for A History of Greek Mathematics, Volume 2: From Aristarchus to Diophantus (Dover Books on Mathematics)

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2, −1, 0, 1, 2, . }. c 2000 by CRC Press LLC intersection: the set A ∩ B of objects common to both sets A and B. intersection relation: for binary relations R and S on A, the relation R ∩ S where a(R ∩ S)b if and only if aRb and aSb. interval (in a poset): given a ≤ b in a poset, a subset of the poset consisting of all elements x such that a ≤ x ≤ b. inverse function: for a one-to-one, onto function f : X → Y , the function f −1 : Y → X whose value at y ∈ Y is the unique x ∈ X such that f (x) = y.

Null set: the set with no elements, written ∅ or { }. omega notation: f is Ω(g) if there are constants C and k such that |g(x)| ≤ C|f (x)| for all x > k. one-to-one (function): a function f : X → Y that assigns distinct elements of the codomain to distinct elements of the domain; thus, if x1 = x2 , then f (x1 ) = f (x2 ). , for every y ∈ Y , there is an x ∈ X such that f (x) = y. OR: the logical operator for disjunction, also written ∨. pairwise disjoint: property of a family of sets that each two distinct sets in the family have empty intersection; also called mutually disjoint.

C 2000 by CRC Press LLC symmetric: the property of a binary relation R that if aRb then bRa. symmetric difference (of relations): for relations R and S on A, the relation R ⊕ S where a(R ⊕ S)b if and only if exactly one of the following is true: aRb, aSb. symmetric difference (of sets): for sets A and B, the set A ⊕ B containing each object that is an element of A or an element of B, but not an element of both. system of distinct representatives: given sets A1 , A2 , . . , An (some of which may be equal), a set {a1 , a2 , .

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A History of Greek Mathematics, Volume 2: From Aristarchus to Diophantus (Dover Books on Mathematics) by Thomas Heath


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