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3. Let r and y be positive real numbers. From the definition of the product ry and from Theorem 1.4.1 of Cranks, we know that lim tn(x) + tn(y) = ity. n-+00 For each real e > 0, find an explicit N(c) so that when n > N(e), we have Itn (I) + tn(y) - (x + y)| 0 there is a natural number N so that an - L N. We sometimes denote L by lim an n-too