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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3What does $\frac{x}{\infty}$ mean? – Michael Albanese Apr 19 '15 at 03:29
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What is $\infty/\infty$? – Daniel W. Farlow Apr 19 '15 at 03:29
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$\infty$ is not a number. You can't count to it. – Mnifldz Apr 19 '15 at 03:35
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@pizza: The posts have similarities but they do not seem to be actual duplicates. – Rory Daulton Apr 19 '15 at 05:15
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@RoryDaulton Close enough for me. – Apr 19 '15 at 05:15
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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.
Prasun Biswas
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