等價關係 equivalence relation
R is an equivalence relation over A×B⇔{R=∼={⟨x,y⟩|x∼y}⊆A×B(e)equivalence 等價⋮⋮⇔⎧⎪
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⎪⎩R={⟨x,y⟩|xRy}⊆A×B(R)relation∀⟨x,y⟩∈R(xRx)(r)reflexive∀⟨x,y⟩∈R(xRy⇒yRx)(s)symmetric∀⟨x,y⟩,⟨y,z⟩∈R({xRyyRz⇒xRz)(t)transitive⇔⎧⎪
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⎪⎩R={⟨x,y⟩|xRy}⊆A×B關係∀⟨x,y⟩∈R(⟨x,x⟩∈R)自反∀⟨x,y⟩∈R(⟨y,x⟩∈R)對稱∀⟨x,y⟩,⟨y,z⟩∈R(⟨x,z⟩∈R)遞移