An easy proof by contradiction concerning sets absorbing sequences; a proof that various statements about convergence of sequences in a non-empty set are equivalent to the set having exactly one point; various examples relating to (non) sequential compactness and divergence of subsequences. Dr Feinstein's blog may be viewed at: http://explainingmaths.wordpress.com Dr Joel Feinstein is an Associate Professor in Pure Mathematics at the University of Nottingham.