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If $\dfrac {x} {\infty }=0,$ where $x$ is a finite number, than wouldn't $0\cdot \infty $ be equal to any number? Making this not work?

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    $\begingroup$ What does $\frac{x}{\infty}$ mean? $\endgroup$ – Michael Albanese Apr 19 '15 at 3:29
  • $\begingroup$ What is $\infty/\infty$? $\endgroup$ – Daniel W. Farlow Apr 19 '15 at 3:29
  • $\begingroup$ $\infty$ is not a number. You can't count to it. $\endgroup$ – Mnifldz Apr 19 '15 at 3:35
  • $\begingroup$ @pizza: The posts have similarities but they do not seem to be actual duplicates. $\endgroup$ – Rory Daulton Apr 19 '15 at 5:15
  • $\begingroup$ @RoryDaulton Close enough for me. $\endgroup$ – user147263 Apr 19 '15 at 5:15
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The problem here is:

Division by $0$ or $\pm\infty$ is not generally defined!

It is not entirely mathematically correct to write $\dfrac{x}{\infty}=0$ when $x$ is real.

One thing you can do to mathematically justify your initial statement is to write it in the form of a limt:

$$\lim_{n\to\infty}\frac{x}{n}=0~\forall~x\in(-\infty,+\infty)$$

And then, you can write your claim (also in the form of a limit):

$$\lim_{n\to\infty}(0\times n)=0$$

Without using the form of limit, the values are undefined.

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