I understand why this result is given for 1/(1/0)
(1/0 equals ? in the Riemann sphere), but here I am talking about 0/(0/0)
.
https://www.wolframalpha.com/input/?i=0/%280/0%29
We could, of course, simply understand 0/0 as a number that multiplied by 0 is 0; every real number fulfills this definition, but even without making it any more specific, it would be clear that 0(1/(|0/0|?+?1)) is 0 because it is clear that 0(1/(|x|?+?1)) equals 0 for every x in the Riemann sphere. However, it still would not be clear that 0/(0/0) equals 0, since while 0 divided by any number except 0 is 0, it is not clear that 0/0 is 0. Wolfram|Alpha does give the result (undefined)
for 0(0/0)
($0\times\infty$ is an indeterminate form), but does not for 1^(0/0)
(although $1^?$ is an indeterminate form as well), 0^(0/0)
($0^0$ is an indeterminate form) and 0/(0/0)
.
This also works using other indeterminate forms, e.g., 1^log(0, 0)
(result: 1
).
Is this intentional? The Wolfram Language, on the other hand, returns Indeterminate
even for 0 (1/(Abs[0/0] + 1))
.