In effect, the terms 'infinite distance' and 'infinite period of time' are meaningless. Both a distance and a period of time must have a size in order to exist. Size implies value - something that infinity does not possess. Infinity' is not measurable. Feel free to respond.
Infinity stands for value without limit.
This means that no value that can be put forth, however large, will ever be equal in value to infinity. There is then the question as to if a number larger than a second number is closer to infinity than the second number. Let us examine this situation more closely. Finite numbers possess value. Value could be said to directly correspond to the size of a number.