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I know that $\frac{1}{0}$ is undefined.

What about $\frac{1}{0}-0.5$ it's undefined as well?

Michael Albanese
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user161260
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    Short answer: Yes. – Demosthene Jan 21 '15 at 12:22
  • Which does not mean, that one can not attach some information to it. WA lists it and $1/0$ as $\tilde{\infty}$, and calls it ComplexInfinity, a quantity with infinite magnitude, but undetermined complex phase. – mvw Jan 21 '15 at 12:31
  • Why wouldn't it be? The motivation for this question is seriously unclear to me. – quid Jan 21 '15 at 12:55

2 Answers2

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An expression is said to be undefined if its meaning or value is not defined. In some cases, an expression is undefined because it is impossible to define it in a consistent or meaningful way; this is the case for the expression $\frac{1}{0}$. No matter how you choose to define the expression $\frac{1}{0}$, it leads to inconsistencies under the usual rules of arithmetic; for that reason, we leave the expression undefined.

In the case of the expression $\frac{1}{0} - 0.5$, if we were to define its value, using the rules of arithmetic (in particular, adding $0.5$), one would obtain a value for $\frac{1}{0}$ which we already know leads to inconsistencies. Therefore, the expression $\frac{1}{0} - 0.5$ is undefined for the same reason that the expression $\frac{1}{0}$ is: there is no way to assign it a value which is consistent with the usual rules of arithmetic.

Michael Albanese
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You know $\frac{1}{0}$ is undefined. So, $\frac{1}{0} - 0.5$ is also undefined. Since $\text{undefined} - 0.5$, is not possible to define. But main interesting thing is to know why $\frac{1}0$ is undefined. For that purpose see this link here.

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A.D
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