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I was watching a video on numberphile about dividing by 0 and It said that x/0=Undefined or Error since it could be + or - ∞. Question is why did mathematicians call it Undefined instead of ±∞? This way if we did 20/0 on a calculator it would give us ±∞ instead of Error.

Also if you said to someone that x/0=±∞ would you be right or wrong?

iProgram
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2 Answers2

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According to that video, the method utilized holds that if you approach for the right you get $+\infty$ but if you approch for the left you get $-\infty$. If we define this two terms (because infinity is not a number, is a concept) as different (infinity to the left is different to infinity to the right) you get two different answers. And you can't have two different answers for division, because division is an operator defined to have only one answer.

3d0
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  • And the reason $\infty$ isn't a real number is because then $\infty \cdot 0$ would have infinitely many solutions and that would crush some of the nice properties real numbers have. – kingW3 Feb 19 '15 at 17:57
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$\pm \infty$ is:
i) not a real number
ii) two concepts.
If $\frac{20}{0}$ were to yield two "answers", neither of which were real numbers, would that match your intuition as to what it means to have a defined value?

Sloan
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  • So you mean x/0 ≠±∞because it is not a real number? – iProgram Feb 19 '15 at 17:38
  • Consider the grammar of your comment carefully. What determiner did you use before "real number", and in what way is that article not appropriate considering the answer I initially provided? Answering this should provide further insight into what has been posted here so far. – Sloan Feb 19 '15 at 17:47
  • I just thought that was what you meant. Never mind – iProgram Feb 19 '15 at 17:51
  • It was one facet of what I meant. $\pm \infty$ is two separate concepts, neither of which are numbers. Hence "a real number" in your comment doesn't follow, as "a real number" is singular, but $\pm \infty$ is plural. – Sloan Feb 19 '15 at 17:57