Hidden Variables Math Example 4

Solution

1. 1
   Solution: $x = 4$ regardless of domain.
2. 2
   Hidden variable: the domain. For $\mathbb{N}$: $x = 4$ is valid. For $\mathbb{R}$: $x = 4$ is also valid.
3. 3
   Now consider $x + 3 = 2$: for $\mathbb{N}$ (positive integers), $x = -1$ which is not in $\mathbb{N}$ — no solution. For $\mathbb{Z}$ or $\mathbb{R}$: $x = -1$ is valid.
4. 4
   The domain is a hidden variable that determines whether a solution exists.