Without an abstraction of this sort, even the famous Greek paradoxes would not make sense. The moment the distance between the turtoise and Achilles becomes smaller than the latter's foot length, he will simply step on the turtoise and end the competition. For 2000 years, however, people pondered over the paradox which was based on the assumption that the turtoise and Achilles are able to make an infinite number of steps.

I disagree. Claiming that a dog that is standing still is "running at an infinite speed" is obviously wrong.

I ain't any wiz but I think relativity is the factor. From man point of view, dog is coming to him and vice-versa, I guess.

Even if the dog was going at an infinite speed it wouldn't be moving and therefore have a sspeed of zero.
Infinity(speed)x 0(distance)=zero

I also agree with that guy who said the problem should be inturpurated as the dog and man were both geometric points, in which case there would be no way the dog could be travelling at an infinite speed.

this is true, yet in our case, the speed is lim s
s→ ∞
and the distance is lim d
d→0

thus the speed is ALMOST infinite, and the distance is ALMOST zero.