How is this conversation possible?

Question

I recently came upon an inequality, where the writer did something like this :-

$$\frac{-1}{2}<2^{-x}<4$$ $$\Rightarrow0<2^{-x}<2^2$$

He turned $\frac{-1}{2}$ to $0$. How is this possible? Please explain

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Link of question

Answer 1

$2^{-x}>0$ regardless of the value of $x$. The writer just ignored the lower bound $-\frac12$ because it brings no information at all, and replaced it with the sharper bound 0.