An old explanation, for an old saying...

There's an old saying 'close enough for all practical purposes...' which has a very good physical model/explanation.
If you are in a classroom with an equal number of males and females, separate the two sets and have all the males stand on one side of the room, and all the females on the other.
At a given command, have each set of people move toward each other, so that each line of people exactly halves the distance between them.
In theory, no matter how many times you repeat this command, the two groups will never reach each other...
In practice, you will find that after a relatively few number of instances, the two groups will be close enough together 'for all practical purposes.'   :)