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Is $1/(1/0)$ undefined, or does it equal zero? By one way of thinking, you could say $1/(1/0)=1*0/1=0$ (taking the reciprocal) and thus equals $0$. But by another, the original expression simply cannot be evaluated because there is division by zero. I think it's undefined (with the reciprocal in fraction division merely being a shortcut to calculate the number of times one fraction can go into the other), but many other sources seem to disagree (with others agreeing). Which is correct?

FinnPlayz_
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    whenever part of an expression is undefined, the entire thing is undefined. If you want to write $0$, then just write $0$. – peek-a-boo May 21 '21 at 15:55
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    $1/0$ is meaningless in the real field. Also in the rational field. Or you can say it is not permitted. – 311411 May 21 '21 at 16:04
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    By convention, arithmetic operations within parentheses are to be completed before operations outside of them. By that convention, the expression is undefined. – Keith Backman May 21 '21 at 16:32
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    $1/0$ has not reciprocal, because this is not defined in rational numbers. – Antonio Hernandez May 21 '21 at 16:40
  • To add a complication, if you define $f(x)=1/(1/x)$ in Desmos, and evaluate $f(0)$, Desmos will report that $f(0)=0$, not undefined. – EthanAlvaree Jun 29 '21 at 17:06

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