Is infinity the reciprocal of zero? Is zero the reciprocal of infinity? It would make feeling that they would certainly be--they behave in a similar means (anything multiplied by zero or infinity outcomes in zero or infinity, because that example) and you can"t have actually a number infinity close to zero however not zero (as much as ns know.) Also, my simple understanding of the Riemann sphere seems to imply that because infinity and also zero room opposite poles, they must be reciprocals.

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I do understand that $frac10$ is technically undefined and infinity can"t yes, really be treated like another number, yet could they be reciprocals in part situations?

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

I"m i m really sorry if this is a stupid and also obvious question, my understanding of dearteassociazione.orgematics in the kingdom of infinity is... Shaky come say the least.

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edited Feb 25 "19 at 3:49

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It depends on the number mechanism you"re using.

If you"re using the real numbers or the facility numbers, climate zero has no reciprocal. In other words, $1/0$ is an undefined expression. Also, in this systems, there"s no together number as infinity. In various other words, $infty$ is an undefined symbol.

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

Out of these 4 number systems, the an initial two (the actual numbers and also the complex numbers) space much much more commonly provided than the last two (the projectively expanded real line and the Riemann sphere). So lot so, in fact, the we typically say "division through $0$ is undefined" and "infinity is not a number" without clarifying which device we"re using.

The factor that the an initial two solution are an ext commonly provided is that these 2 systems are fields, and also the various other two space not.