1. The problem is to understand the set $\mathrm{imf} = \left\{ \frac{m+n}{mn} \mid m,n \in \mathbb{N} \right\}$. 2. This set consists of all numbers that can be expressed as the sum of two natural numbers $m$ and $n$ divided by their product. 3. The formula is given by: $$\frac{m+n}{mn}$$ where $m,n$ are natural numbers (positive integers). 4. Important rules: - $m,n \in \mathbb{N}$ means $m,n$ are positive integers. - The denominator $mn$ is never zero since $m,n$ are natural numbers. 5. Let's simplify the expression: $$\frac{m+n}{mn} = \frac{m}{mn} + \frac{n}{mn} = \frac{1}{n} + \frac{1}{m}$$ 6. So every element in the set can be written as the sum of the reciprocals of two natural numbers. 7. For example, if $m=1$ and $n=2$, then: $$\frac{1+2}{1 \times 2} = \frac{3}{2} = 1.5$$ 8. If $m=2$ and $n=3$, then: $$\frac{2+3}{2 \times 3} = \frac{5}{6} \approx 0.8333$$ 9. Therefore, the set $\mathrm{imf}$ contains all numbers of the form $\frac{1}{m} + \frac{1}{n}$ where $m,n$ are natural numbers. Final answer: $$\mathrm{imf} = \left\{ \frac{1}{m} + \frac{1}{n} \mid m,n \in \mathbb{N} \right\}$$