Question Number 195290 by Matica last updated on 29/Jul/23
$$\:{A}\:{professor}\:{said}\:\:\mathrm{0}\mid\mathrm{0}\:{because}\:\mathrm{0}=\:\mathrm{0}×{a}+\mathrm{0}\:\:\:,\:{a}\in\:\mathbb{N}.\:{Can}\:{you}\:{prove}? \\ $$
Answered by Frix last updated on 29/Jul/23
$${a}\mid{b}\:\Leftrightarrow\:\frac{{b}}{{a}}\in\mathbb{Z}\:\mathrm{but}\:\frac{\mathrm{0}}{\mathrm{0}}\:\mathrm{is}\:\mathrm{not}\:\mathrm{defined}\:\Rightarrow\:\mathrm{0}\mid\mathrm{0}\:\mathrm{is}\:\mathrm{meaningless} \\ $$