A1 - 1 What is a rational number Abbott says&A rational...

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Unformatted text preview: 1. What is a rational number ? Abbott says, &A rational number is any number that can be expressed in the form p=q where p and q are integers.¡ You can call p=q a ratio or a quotient or a fraction if you want. You can add that q 6 = 0 . But you can¢t require that p and q be natural numbers, because you don¢t get or the negative rational numbers that way. I suppose it¢s okay to require q > , but Abbott doesn¢t and I don¢t think most people do. However, I don¢t think it¢s okay to require that p and q have no common integer factors except 1 and & 1 . It¢s true that you can arrange for that to happen, but it¢s not part of the de£nition of a rational number. The way you multiply two rational numbers is by using the formula a b ¡ c d = ac bd so 3 2 ¡ 4 7 = 12 14 Do we have to cancel the common factor of 2 before we can say that 12 = 14 is a rational number? 2. State Theorem 1.1.1, the &rst theorem in the text ....
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A1 - 1 What is a rational number Abbott says&A rational...

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