<p>Definition:<br />x₀ is a limit point of a set S of real numbers if

Question

<p>Definition:<br />x₀ is a limit point of a set S of real numbers iff:<br /><br /><img src="https://s3.amazonaws.com/answer-board-image/cramster-equation-201153117276344001764705955228004.gif" alt="" align="absMiddle" /><br /><br />1. Provide an example of a set S of real numbers which has a limit point which is contained in S, and use the above definition to prove that the point in question is really a limit point.<br /><br />2. Provide an example of a set S of real numbers which has a limit point which is not contained in S, and use the above definition to prove that the point in question is really a limit point.<br /><br />3. Provide an example of a set S of real numbers which has no limit points, and justify based on the definition.</p>

Explanation / Answer

It is a little hard to read your question, but: S=[0,1] every point in S is a limit point S=(0,1) 0 and 1 are limit points but they aren't in S S={1,2,3} has no limit points.

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