Suppose sequence (an) is bdd and div. Prove (an) has at least 2 conv subseq that conv to diff numbers
By BWT, we know it has at least one conv subseq
Assume (an) conv. Then every subseq must conv to exactly one limit.
This means (an) must have at least 2 conv subseq that conv to diff numbers.
This feels too short and yet it seems like I have all the info I need in there. Is this good?