Regarding logic. Consider the tortoise and the hare. Near the end of the race, the hare realises that the tortoise might win, so decides to start running again. The hare sees the tortoise in the distance, so runs to that point. He takes a finite amount of time to reach that point, but in that time, the tortoise has moved on a finite distance. The Hare then takes a finite time to run to that point, but the tortoise has also moved on a little bit in that time. The hare runs to the point where the tortoise is now, but again, the tortoise has used that time to move on a bit! So the hare runs to the point where the tortoise is now, but the tortoise has gone on a bit again! This goes on and on and on, and if you add up all the small bits of time the hare has travelled to "catch up" with the tortoise, it will be infinity! I.e. it takes the hare an infinite amount of finite bits of time to catch the tortoise up, and so cannot catch up with the tortoise, ever!
Clearly, this isn't right, yet it makes logical sense.
Analogy and logic can be used to prove anything. That is its great power, and it's greatest weakness.