Question Number 56705 by gunawan last updated on 22/Mar/19
$$\mathrm{the}\:\:\mathrm{smallest}\:\mathrm{value}\:\mathrm{of} \\ $$$$\mathrm{S}=\left\{\:^{\mathrm{3}} \sqrt{{n}}−^{\mathrm{3}} \sqrt{{m}}\:\mid\:{n},\:{m}\:\in\mathbb{N}\right\}\:\:\mathrm{is}... \\ $$
Answered by kaivan.ahmadi last updated on 25/Mar/19
$${S}\:{has}\:{no}\:{smallest}\:{value}\:{of}\:\:{the} \\ $$$${form}\:{of}\:{the}\:{number},\:{since}\:\: \\ $$$${if}\:{n}=\mathrm{0}\:{then} \\ $$$${li}\underset{{m}\rightarrow\infty} {{m}S}=−\infty \\ $$