Lol what? I think I just had a brain fart... How can it depend on the behavior of infinite if it is infinite in the first place? To my understanding it's either finite or not. :/ math and I never got along...
Let's explain this graphically without bursting your brain In this case of convergent infinity:
If you graph 1/x, notice the two curves? As you go along the positive x-axis, you can imagine the 1/x curve in the first quadrant approaching or getting "closer" towards touching the x-axis as the positive x coordinate values increase to infinity. We say the limit is 0 because 1/x is becoming more like 0 as x increases. Paradoxically, we say the limit is 0, but, theoretically, the 1/x curve never ever touch the y=0 (or x-axis).....because it's is *infinitely* approaching the x-axis.
Divergent is when the values of a function/curve increases without any bound or approaching any value such as the example above. The values becomes infinite
Hope this enlightens you, iSign? Let me know if you have questions.