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We show that the set $\ell^{\infty}\setminus c_0$ is dense-lineable anddense-algebrable answering a question posed by Nestoridis and complementing aresult by Garc\'ia-Pacheco, Mart\'in and Seoane-Sep\'ulveda.

Dense Lineability and algebrability of $\ell^{\infty}\setminus c_0$