# a problem of an infinite long running race

suppose A and B are two people,they can live forever,will never die.if omega exists really,one day,the have an omega-metre long run race on a straight road more than omega metres long.BOTH A and B run a step per second,but A runs 2m per step,B runs 1m per step.clearly B runs slower than A,so the distance between A and B will be further and further.but in ordinal arithmetic we know that 2*omega=omega,so A and B will finish the race in the same time,omega seconds.the question is,how can B finally catch up A?

• – Drux
Commented Mar 21, 2014 at 13:04
• You cannot "finish" an infinite long race ... After a finite amount of time (let N seconds) A will be far ahead to B but he still have to run for an infinite amount of time. And you cannot either stay at the finishing line waiting for the winner : for also if you started your travel well in advance with respect to the start of the race, you will never reach the end... Commented Mar 21, 2014 at 13:13