This exercise is designed to convince you that 1/0 and 0/0 could not ever adequately define a
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Question:
This exercise is designed to convince you that 1/0 and 0/0 could not ever adequately define a real number.
(a) Suppose 1/0 were a real number, say 1/0 = x ? R. Deduce the contradiction 0 = 1.
(b) Suppose that 0/0 were a real number, say 0/0 = x ? R. Let y be any other real number. Prove that 0/0 = y as well, so that 0/0 does not uniquely determine one real number.
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