Recall that Q is closed under addition and multiplication. That is, if a, b e Q...

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Recall that Q is closed under addition and multiplication. That is, if a, b e Q then a + b = Q and ab e Q. 1. Recall that I is the set of all irrational numbers, that is I (xER:*#Q) (a) Let a e Q and te I. Prove that a + tel and at e I provided a 40. (b) Is I closed under addition and multiplication? Given two irrational numbers s and t, what can we say about s+t and st? Give proofs or counterexamples to verify your results. (c) Prove that I is dense in R. That is, for real numbers a < b prove that there exists t e I such that a < t < b. Hint: consider the real numbers a- -2 and b-2. Recall that Q is closed under addition and multiplication. That is, if a, b e Q then a + b = Q and ab e Q. 1. Recall that I is the set of all irrational numbers, that is I (xER:*#Q) (a) Let a e Q and te I. Prove that a + tel and at e I provided a 40. (b) Is I closed under addition and multiplication? Given two irrational numbers s and t, what can we say about s+t and st? Give proofs or counterexamples to verify your results. (c) Prove that I is dense in R. That is, for real numbers a < b prove that there exists t e I such that a < t < b. Hint: consider the real numbers a- -2 and b-2.

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a Lets prove that if a is a rational number a Q and t is an irrational number t I then a t and at are irrational numbers Proof Assume a is a rational ... View the full answer