Mathematical/ sports question ?

Question

This is one of those questions that made no sense in school like "Train A and Train B."

Though this may never happen in a football game it still is in the back of my mind.

Say you have a personal foul Face Mask call on you opponents 10 yard line. The result of the call would be half the distance to the goal and an automatic first down.

Say this happened over and over again for infinity without the offense running a single play.

Is it fair to say that the ball will never cross the goal line?

Half of 10 would put it on the 5

5 would be 2.5

2.5 would be 1.25

and so on...

Answer 1

Great! The ancient Greeks called that one of Zeno's paradox! You have discovered the basis for infinitesimal calculus!