Basically 0/0 can be anything. Unless we tend to go beyond normal understanding of infinity, we can actually get 0/0=1. For example
Taking natural long on both sides yields
If we could consider the "undefined" cancelling each other equal to zero.
We can argue like forever with this thing but this is how mathematics progresses Perhaps 0/0=An Apple:)
You get funny values when you take all the infinities as the same. Infinity as a concept gives rise to many problems like S=1-1+1-...infinity=1/2 because we tend to take all the infinities as the same like (1+infinity)=infinity. What is the value of infinity/infinity? I am more to the concept that the Infinity has an origin and point of reference. For example, if we had a source of light that could travel forever into the infinity and is set to travel today and the another one would be set to travel tomorrow, are they the same value when they reach infinity?
If they do have the same value, I can show you that Riemman zeta functionnot and many more.