Plane Geometry - Bruce E. Shapiro
Plane Geometry - Bruce E. Shapiro Plane Geometry - Bruce E. Shapiro
24 SECTION 5. LOGIC AND PROOF“I ♥ Geometry!”« CC BY-NC-ND 3.0. Revised: 18 Nov 2012
Section 6The Real NumbersWe will take the terms set and element as undefined terms. We write aset as the list of elements surrounded by curly brackets:or by a rule{A, B, C, ...}{x|S(x)}where S(x) is some rule such as “x is even.”We use x ∈ S to represent “x is an element of the set S.”We denote the natural numbers bythe integers byand the positive integers byN = {1, 2, 3, . . . },Z = {. . . , −3, −2, −1, 0, 1, 2, 3, . . . },Z + = {0, 1, 2, ..}The union of two sets S and T is given byS ∪ T = {x|x ∈ S ∧ x ∈ T }0 This section is intended primarily as a review and hence is necessarily concise.25
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Section 6The Real NumbersWe will take the terms set and element as undefined terms. We write aset as the list of elements surrounded by curly brackets:or by a rule{A, B, C, ...}{x|S(x)}where S(x) is some rule such as “x is even.”We use x ∈ S to represent “x is an element of the set S.”We denote the natural numbers bythe integers byand the positive integers byN = {1, 2, 3, . . . },Z = {. . . , −3, −2, −1, 0, 1, 2, 3, . . . },Z + = {0, 1, 2, ..}The union of two sets S and T is given byS ∪ T = {x|x ∈ S ∧ x ∈ T }0 This section is intended primarily as a review and hence is necessarily concise.25
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