Is $\max \left (\frac{2}{\Vert w \Vert} \right )$ the same as $\min(\Vert w \Vert)$?

Question

I was reading this article on support vector machines (SVMs), which claims

$$\max \left (\frac{2}{\Vert w \Vert } \right) = \min(\Vert w \Vert)$$

How can that possible be? What happened to $2$? Even one teacher claimed the same

Answer 1

Let $0 < a < b$. Note that

$$\underset{x \in [a,b]}{\operatorname{argmax}} \frac2x = a = \underset{x \in [a,b]}{\operatorname{argmin}} x$$ even though

$$\frac2a = \underset{x \in [a,b]}{\max} \frac2x \color{blue}{\neq} \underset{x \in [a,b]}{\min} x = a$$