How is $0\cdot\infty= -1$? It is known that the product of slopes of two perpendicular lines is equal to $-1$ ($m_1*m_2=-1$ for $m_1$ and $m_2$ being the slopes of the perpendicular lines $l_1$ and $l_2$). The slope of $x$-axis $=0$; the slope of $y$-axis$=$ undefined (or $\infty$); $x$-axis and $y$-axis are perpendicular to each other. So, it must mean that the product of their slopes (i.e. $0$ and $\infty$) must be equal to $-1$. How is $0*\infty=-1$? Is it really?


How is $0*\infty=-1$? Is it really?

No, $0$ times $\infty$ is not equal to $-1$. In fact, the product isn't even defined. It is not a question of this somehow giving a contradiction, it just isn't defined.
The rule you are referring to says that: Given two lines with slopes $m_1$ and $m_2$ (real numbers) then
the lines are perpendicular if and only if their product is $-1$.
So, it is part of the assumption in the rule that the slopes be real numbers, and $\infty$ is not a real number.
