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:Then, for every ''n'', ||''f''<sub>''n''</sub>||<sub>''Y''</sub> = ||''f''<sub>''n''</sub>||<sub>∞</sub> = ''n'', but
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:Hence, no constant ''C'' can be found such that ||''f''<sub>''n''</sub>||<sub>''Y''</sub> ≤ ''C''||''f''<sub>''n''</sub>||<sub>''X''</sub>, and so the embedding of ''X'' into ''Y'' is discontinuous.
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