Is infinity the mutual of zero? Is zero the mutual of infinity? It would certainly make sense that they would be--they act in a similar method (anything multiply by zero or infinity outcomes in zero or infinity, because that example) and you can"t have a number infinity close come zero however not zero (as much as ns know.) Also, my straightforward understanding that the Riemann sphere seems to suggest that due to the fact that infinity and also zero room opposite poles, they must be reciprocals.

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I do understand that $frac10$ is technically undefined and also infinity can"t really be treated like an additional number, however could they it is in reciprocals in part situations?

So, is $frac1infty$ some infinitesimal, or is it zero? and also does $frac10=infty$?

I"m sorry if this is a stupid and obvious question, my knowledge of in the realm of infinity is... Shaky come say the least.

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edited Feb 25 "19 in ~ 3:49

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It counts on the number system you"re using.

If you"re making use of the genuine numbers or the complex numbers, then zero has no reciprocal. In various other words, $1/0$ is an unknown expression. Also, in this systems, there"s no such number as infinity. In other words, $infty$ is an unknown symbol.

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If you"re making use of the projectively extended real heat or the Riemann sphere, then the mutual of zero is infinity, and the reciprocal of infinity is zero. In other words, $1/0 = infty$ and also $1 / infty = 0$. (Note the the reciprocal of infinity is exactly zero, not infinitesimal. No one of these four number systems contain any type of infinitesimal numbers.)

Out of these four number systems, the an initial two (the genuine numbers and the complex numbers) are much much more commonly offered than the last 2 (the projectively expanded real line and the Riemann sphere). So lot so, in fact, the we commonly say "division through $0$ is undefined" and "infinity is no a number" without clarifying which mechanism we"re using.

The factor that the very first two equipment are more commonly supplied is the these 2 systems space fields, and also the other two space not.