Great layman explanation! I'd suggest one extremely minor modification to your ping-pong metaphor: Cauchy sequences don't necessarily have to bounce back and fo

Great layman explanation! I'd suggest one extremely minor modification to your ping-pong metaphor: Cauchy sequences don't necessarily have to bounce back and forth between being smaller than your target point and being larger than your target point. They can always increase, or always decrease, too. To give a concrete example, one possible Cauchy sequence for the square root of 2 would just be {1, 1.4, 1.41, 1.414, 1.4142, 1.41421, ...}