Last updates: 7 December 2009
Prove that a real sequence can have at most one limit. | |
Prove that every convergent sequence is Cauchy. | |
Prove that every Cauchy sequence which has a convergent subsequence is itself convergent. | |
Prove that every Cauchy sequence is bounded. | |
Prove that every convergent sequence is bounded. | |
Prove that a contractive sequence is Cauchy. | |
Prove that a contractive sequence is convergent. |
[BG] A. Braverman and D. Gaitsgory, Crystals via the affine Grassmanian, Duke Math. J. 107 no. 3, (2001), 561-575; arXiv:math/9909077v2, MR1828302 (2002e:20083)