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Dividing by exactly 0 is undefined because it's approaching either + or - infinity and diverging. But in this case we're clearly approaching the limit of 0 from strictly the positive side and the intuitive result is to approach + infinity. Just my opinion. It's your game. You can do what you want. But I don't think it's strictly incorrect to colloquially say infinity in this case?
Dividing a number by zero is asking "how many times can we take zero away from this number before it's all gone". Taking infinity zeros away from the number still won't do that, any more than taking zero away once will - infinity isn't really a more "correct" answer than one.
The answer is "there is no such value" - which in mathmatical terms is "undefined".
To put it another way, saying that, say 100 divided by zero is infinity means you're saying that infinity times zero is 100. This isn't true regardless of which infinite number you're meaning by "infinity" (which is not itself a number but a concept).
There are some more in-depth answers here some of which go into why treating the answer as a positive or negative infinite number can still end up at contradictions (the...
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