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i am having trouble working through this. from the definitions, i know that for D to be continuous at 0, we need that ||D(p) - D(0)||

_{u}approaches 0 as ||p||

_{u }approaches 0. This is also equivalent to finding a sequence of polynomials p

_{n }in Z such that ||p

_{n}|| approaches 0 implies ||D(p

_{n})|| approaches 0. So to show discontinuity, i need to find a sequence p

_{n}where ||p

_{n}|| approaches 0 but ||D(p

_{n})|| does not. however i am having trouble coming up with such a sequence.

can someone give me some hints on how to approach this problem?