I suppose it depends on one's definition of "closer". If you define A is closer to X than B as abs(X-A) < abs(X-B), or rather abs(X-B) - abs(X-A) > 0, which is

I suppose it depends on one's definition of "closer". If you define A is closer to X than B as abs(X-A) < abs(X-B), or rather abs(X-B) - abs(X-A) > 0, which is what I would be inclined to do, and take the limit as X goes to infinity, than yes, 10 is closer to +inf than 1. Assuming that X > A and X > B (a fair assumption in this case), this becomes X-B - (X-A) > 0, or rather A - B > 0. Taking the limit as X goes to infinity, this is unchanged, and as such one could say that A is closer to infinity than B iff A>B. As 10 > 1, 10 is closer to infinity than 1. Unfortunately, although I cannot come up with an example offhand, I am fairly sure that there is a proof the other way as well. Infinity is just weird like that.