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Question Number 204123 by Ari last updated on 06/Feb/24

Commented by Rasheed.Sindhi last updated on 06/Feb/24

$$0isevenbecause{it}^{\prime }sdivisibleby2$$

Answered by Frix last updated on 07/Feb/24

$$\mathrm{\forall }a\in \mathbb{Z}:(b=2a\iff b\mathrm{is}\mathrm{even})\wedge (c=2a+1\iff c\mathrm{is}\mathrm{odd})$$$$\Rightarrow$$$$\mathrm{Test}\mathrm{for}x\in \mathbb{Z}:\{\begin{array}{l}\frac{x}{2}\in \mathbb{Z}\Rightarrow x\mathrm{is}\mathrm{even}\\ \frac{x-1}{2}\in \mathbb{Z}\Rightarrow x\mathrm{is}\mathrm{odd}\end{array}$$$$x=0:\{\begin{array}{l}\frac{0}{2}=0\in \mathbb{Z}\Rightarrow 0\mathrm{is}\mathrm{even}\\ \frac{0-1}{2}=-\frac{1}{2}\notin \mathbb{Z}\Rightarrow 0\mathrm{is}\mathrm{not}\mathrm{odd}\end{array}$$

Answered by BaliramKumar last updated on 06/Feb/24

$$\mathrm{smallest}\mathrm{even}\mathrm{whole}\mathrm{number}\mathrm{is}=0$$$$\mathrm{smallest}\mathrm{even}\mathrm{natural}\mathrm{number}\mathrm{is}=2$$$$\mathrm{smallest}\mathrm{even}\mathrm{number}\mathrm{is}=2\left[\mathrm{Generally}\right]$$$$\mathrm{but}\mathrm{smallest}\mathrm{even}\mathrm{number}\left(\mathrm{integer}\right)\mathrm{is}\mathrm{not}\mathrm{defiened}$$$$-2,-10,-6666\mathrm{all}\mathrm{are}\mathrm{even}\mathrm{number}$$

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