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I understand that infinity is not a number and you can't just multiply it with another number, but for example whilst calculation limit of a function, I come across some number times infinity and I get infinity as a final answer, but what happens when you multiply infinity with a negative number, and again I am only asking for the sake of calculating limit, I have come to point where my limit is $-8*\infty$ and don't really know what to do with it, logically it seems to be $-\infty$, but is it?

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    $\begingroup$ From the definition of a limit, you can show that $\lim(-a)=-\lim a$. $\endgroup$ – Yves Daoust Feb 6 '17 at 19:59
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In a hand-wavy sort of way: yes.

$$\lim_{x \to +\infty} -8x = -\infty.$$

This is read as: "The limit of negative $8x$, as $x$ approaches (positive) infinity, is negative infinity."

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