Convergence divergence

• Can a Double Sequence Have Different Iterated Limits?
  A double sequence can have different iterated limits: for aₘₙ = m/(m+n), the two orders give 0 and 1, so no joint limit exists.
• Can a Convergent Sequence Be Unbounded?
  No: every convergent real sequence is bounded. Bound its tail using the limit, then take a maximum over the finitely many earlier terms.