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prove that {1/n} n=1 to inf is not compact in R with usual metric. suppose use the adjoint point {0} to {1/n} n=1 to inf

Question

prove that {1/n} n=1 to inf is not compact in R with usual metric. suppose use the adjoint point {0} to {1/n} n=1 to inf
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Solution 1

To prove that the set {1/n} for n=1 to infinity is not compact in R with the usual metric, we can use the concept of open covers and the property that a set is compact if and only if every open cover has a finite subcover.

Step 1: Define the set A = {1/n} for n=1 to infinity and include the point 0 Knowee AI is a powerful AI-powered study tool designed to help you to solve study problem.

Knowee AI  is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI  is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI  is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI  is a powerful AI-powered study tool designed to help you to solve study problem.
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