"Infinitely repeating decimals may not exit, they may terminate somewhere down the line but we can never tell."
I've heard it claimed that numbers that pi or e may terminate eventually and that there is no way of knowing.
Is there no mathematical way to show that a non-rational non-terminating decimal will have infinitely many digits and that it cannot possibly ever terminate?
Do we only proclaim pi to be non-terminating because we've "never reached the final decimal place?" That can't be, can it?