Question Number 204123 by Ari last updated on 06/Feb/24
Commented by Rasheed.Sindhi last updated on 06/Feb/24
$$\mathrm{0}\:{is}\:{even}\:{because}\:{it}'{s}\:{divisible}\:{by}\:\mathrm{2} \\ $$
Answered by Frix last updated on 07/Feb/24
$$\forall{a}\in\mathbb{Z}:\:\left({b}=\mathrm{2}{a}\:\Leftrightarrow\:{b}\:\mathrm{is}\:\mathrm{even}\right)\wedge\left({c}=\mathrm{2}{a}+\mathrm{1}\:\Leftrightarrow\:{c}\:\mathrm{is}\:\mathrm{odd}\right) \\ $$$$\Rightarrow \\ $$$$\mathrm{Test}\:\mathrm{for}\:{x}\in\mathbb{Z}:\:\begin{cases}{\frac{{x}}{\mathrm{2}}\in\mathbb{Z}\:\Rightarrow\:{x}\:\mathrm{is}\:\mathrm{even}}\\{\frac{{x}−\mathrm{1}}{\mathrm{2}}\in\mathbb{Z}\:\Rightarrow\:{x}\:\mathrm{is}\:\mathrm{odd}}\end{cases} \\ $$$${x}=\mathrm{0}:\:\begin{cases}{\frac{\mathrm{0}}{\mathrm{2}}=\mathrm{0}\in\mathbb{Z}\:\Rightarrow\:\mathrm{0}\:\mathrm{is}\:\mathrm{even}}\\{\frac{\mathrm{0}−\mathrm{1}}{\mathrm{2}}=−\frac{\mathrm{1}}{\mathrm{2}}\notin\mathbb{Z}\:\Rightarrow\:\mathrm{0}\:\mathrm{is}\:\mathrm{not}\:\mathrm{odd}}\end{cases} \\ $$
Answered by BaliramKumar last updated on 06/Feb/24
![smallest even whole number is = 0 smallest even natural number is = 2 smallest even number is = 2 [Generally] but smallest even number(integer) is not defiened −2, −10, −6666 all are even number](https://www.tinkutara.com/question/Q204128.png)
$$\mathrm{smallest}\:\mathrm{even}\:\mathrm{whole}\:\mathrm{number}\:\mathrm{is}\:=\:\mathrm{0} \\ $$$$\mathrm{smallest}\:\mathrm{even}\:\mathrm{natural}\:\mathrm{number}\:\mathrm{is}\:=\:\mathrm{2}\:\:\:\: \\ $$$$\mathrm{smallest}\:\mathrm{even}\:\mathrm{number}\:\mathrm{is}\:=\:\mathrm{2}\:\:\:\:\:\:\:\left[\mathrm{Generally}\right] \\ $$$$\mathrm{but}\:\mathrm{smallest}\:\mathrm{even}\:\mathrm{number}\left(\mathrm{integer}\right)\:\mathrm{is}\:\mathrm{not}\:\mathrm{defiened} \\ $$$$−\mathrm{2},\:−\mathrm{10},\:−\mathrm{6666}\:\mathrm{all}\:\mathrm{are}\:\mathrm{even}\:\mathrm{number} \\ $$