Discrete Mathematics

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In fact it is sobering to realize that the Italian mathematicians of the fifteenth and sixteenth centuries referred to negative numbers—in their formal writings—as “fictitious” or “absurd.” Mathematics is, in part, a subject that we must get used to. Then 1. lim j→∞ (a j ± b j ) = lim j→∞ a j ± lim j→∞ b j       2. lim j→∞ a j · b j = lim j→∞ a j · lim j→∞ b j CHAPTER 12 3. lim j→∞ aj bj = Sequences lim j→∞ a j lim j→∞ b j 251 provided that 4. lim j→∞ α · a j = α · lim j→∞ a j 5. lim j→∞ a j is unique lim j→∞ b j = 0 for any real number α Insight: In what follows we will generally not mention Part 5 explicitly, but we use it frequently.

Pages: 555

Publisher: Harpercollins College Div; 2nd edition (June 1993)

ISBN: 0673462870

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