Kuratowski gave the following definition of an ordered pair: (a,b)= {{a}, {a,b}}. a) Show: for all...

 

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Kuratowski gave the following definition of an ordered pair: (a,b)= {{a}, {a,b}}. a) Show: for all objects a1, a2, b1,b2, we have (a₁.b₁) = (a2, b₂) exactly when a₁ = a2 and b₁ b₂. Thus Kuratowski's defiition meets our requirement for an ordered pair. b) Do you have any comments or reservations about this definition? (E.g.: is this the only possible definition, or can you think of other reason- able ones? Do you find this definition helpful?) Kuratowski gave the following definition of an ordered pair: (a,b)= {{a}, {a,b}}. a) Show: for all objects a1, a2, b1,b2, we have (a₁.b₁) = (a2, b₂) exactly when a₁ = a2 and b₁ b₂. Thus Kuratowski's defiition meets our requirement for an ordered pair. b) Do you have any comments or reservations about this definition? (E.g.: is this the only possible definition, or can you think of other reason- able ones? Do you find this definition helpful?)

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