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I restarted my analysis book from page 1 trying to relearn everything because I feel like my knowledge is too fragmented. This true false question asks exactly what the title says. I don't know 100% whether it is true or false but I was wondering if this counter example I just thought of works to disprove the statement:

Does the set {3, 3.1, 3.14, 3.141, 3.1415, ...} disprove the statement? Every term is a real number, it is non empty, it's bounded above by 4, and I don't think there is a largest element because it's an infinite set.

Am I wrong? If so, I would greatly appreciate some guidance.

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    True true thanks2012-10-27

1 Answers 1

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Indeed the set you suggest does not have a maximal element, its supremum is in fact $\pi$.

For a simpler example take $(0,1)$.