Well, since you cannot be both alive and dead at the same time (not talking about zombies...), a person must either be alive or dead. The definition of Infinity can be controversial.
1. infinity can describe a number that is so large that nobody can count up to it. So if the unimaginably large amount of health was greater than the damage dealt, then the person would still be alive. Opposite result with the opposite case.
2. But here's another possibility. Infinity has no end. So...if you have no end of health, then you cannot die. No matter how much damage (even infinite damage), your health will not run out, so the person will always be alive.
3. Here is the final one. There is no answer to this question. Infinity is (arguably) not a number. So my answer would be 'none of the above.'
I don't really know how to answer this question, so I included three possible answers. 
