We show that the set $\ell^{\infty}\setminus c_0$ is dense-lineable and dense-algebrable answering a question posed by Nestoridis and complementing a result by Garc\'ia-Pacheco, Mart\'in and Seoane-Sep\'ulveda.
Spaceability and algebrability of sets of nowhere integrable functions
Dense lineability and spaceability in certain subsets of $\ell_{\infty}$
Algebrability, non-linear properties, and special functions
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