Question

Is $Z+$ the same as $N$?

Answer 1

Compare both the given sets by enlisting their elements in roster form

$\mathrm{\mathbb{Z}}$ is known to stand for ‘Zahlen’, which is German for ‘numbers’.

$\mathrm{\mathbb{Z}}$ stands for the set of all integers.

$\Rightarrow \mathrm{\mathbb{Z}}=\left\{......-4,-3,-2,-1,0,1,2,3,4,......\right\}$

By adding a $+$ sign at the top we are considering only the positive integers from the set $\mathrm{\mathbb{Z}}$

By doing so we also neglect $\left\{0\right\}$ as it is not a positive integer either.

$\Rightarrow {\mathrm{\mathbb{Z}}}^{+}=\left\{1,2,3,4,5,....\right\}$$...\left(i\right)$

$\mathrm{\mathbb{N}}$ stands for the set of all natural numbers.

$\Rightarrow \mathrm{\mathbb{N}}=\left\{1,2,3,4,5,....\right\}$$...\left(ii\right)$

From $\left(i\right),\left(ii\right)$ we can observe that all the elements in the sets ${\mathrm{\mathbb{Z}}}^{+}$ and $\mathrm{\mathbb{N}}$ are same

Hence, we can conclude that ${\mathrm{\mathbb{Z}}}^{+}$is the same as $\mathrm{\mathbb{N}}$.