4. Let be the space of all bounded real "quences $2, c, so for each there is an M 2 0 with M for' ail For x, y G 100 we let doo(c, y) sup ynl. -We knowthat dN is a metric ond0 a) Prove that this metric is complete, b) Let S ROO be the subspace of 100 consisting Of sequences that are eventually zero (that is for s e S one has sn () for all sufficiently large n). Prove that the closureS consists of all sequences that converge 'to zero as n N.