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.