Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up. Connect and share knowledge within a single location that is structured and easy to search. Is infinity the reciprocal of zero? Is zero the reciprocal of infinity?
It would make sense that they would be--they behave in a similar way anything multiplied by zero or infinity results in zero or infinity, for example and you can't have a number infinity close to zero but not zero as far as I know.
Also, my basic understanding of the Riemann sphere seems to imply that since infinity and zero are opposite poles, they must be reciprocals. I'm sorry if this is a stupid and obvious question, my understanding of mathematics in the realm of infinity is If you're using the real numbers or the complex numbers, then zero has no reciprocal.
Also, in these systems, there's no such number as infinity. If you're using the projectively extended real line or the Riemann sphere , then the reciprocal of zero is infinity, and the reciprocal of infinity is zero. Note that the reciprocal of infinity is exactly zero, not infinitesimal. None of these four number systems contain any infinitesimal numbers. Out of these four number systems, the first two the real numbers and the complex numbers are much more commonly used than the last two the projectively extended real line and the Riemann sphere.
The reason that the first two systems are more commonly used is that these two systems are fields , and the other two are not. Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more. Ask Question. Asked 2 years, 8 months ago. Active 8 months ago. Viewed 2k times.
Rob 2 2 silver badges 14 14 bronze badges. If you're using the real numbers or the complex numbers, then zero has no reciprocal. Also, in these systems, there's no such number as infinity.
If you're using the projectively extended real line or the Riemann sphere, then the reciprocal of zero is infinity, and the reciprocal of infinity is zero. Note that the reciprocal of infinity is exactly zero, not infinitesimal.
None of these four number systems contain any infinitesimal numbers. Out of these four number systems, the first two the real numbers and the complex numbers are much more commonly used than the last two the projectively extended real line and the Riemann sphere.
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