Question Number 133279 by greg_ed last updated on 20/Feb/21
$$\boldsymbol{\mathrm{hi}},\:\boldsymbol{\mathrm{everybody}}\:! \\ $$$$\boldsymbol{\mathrm{with}}\:\boldsymbol{\mathrm{n}}\:\in\:\mathbb{N}, \\ $$$$\boldsymbol{\mathrm{prove}}\:\boldsymbol{\mathrm{that}}\::\:\exists\:\boldsymbol{\mathrm{n}}_{\mathrm{0}} \:\in\:\mathbb{N}\:/\:\forall\:\boldsymbol{\mathrm{n}}\:\geqslant\:\boldsymbol{\mathrm{n}}_{\mathrm{0}} \:,\:\boldsymbol{\mathrm{n}}^{\mathrm{2}} \:\leqslant\:\mathrm{2}^{\boldsymbol{\mathrm{n}}} . \\ $$