What is a mole? Write two equations for a mole.

(N/A) mole is defined as the amount of substance that contains as many elementary entities as there are atoms in $0.012 \ kg$ of carbon-$12$. At standard temperature and pressure $(STP)$,the mass contained in $22.4 \ L$ volume of an ideal gas is equal to its molecular mass. Its symbol is $mol$.
Equation $1$: In terms of mass,if $M$ is the mass of the gas and $M_{0}$ is the molar mass,the number of moles $\mu$ is given by:
$\mu = \frac{M}{M_{0}}$
Equation $2$: In terms of the number of molecules,if $N$ is the total number of molecules and $N_{A}$ is the Avogadro constant $(6.022 \times 10^{23} \ mol^{-1})$,the number of moles $\mu$ is given by:
$\mu = \frac{N}{N_{A}}$