consider the sequence 1/2, 1/3, 2/3, 1/4, 2/4, 3/4, 1/5, 2/5, 3/5, 4/5, 1/6, ...
for which numbers [tex]\alpha[/tex] is there a subsequence converging to [tex]\alpha[/tex]?
none that i can think of...
The Attempt at a Solution
i think the [tex]\alpha[/tex] values are 1 and 0, but i'm not sure how i can tell if those are the only numbers that subsequences can converge to. what kind of method should i use to determine the values. to get 1 and 0, i just kind of stared at the numbers for a bit, but i'd like to refrain from doing that.