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asymptotically reach it which means it will take an infinte amount of time to cover the final infinitely small distance
Which in practice means you'll never reach your goal.
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Nope , I dont agree
It will not take an infinite amount of time
If you shorten your step each time , the number of steps tend to "infinite " that's true , but the lenght to "zero" thus also the interval of time to cover each step tends to zero
This is the tricky part of the Zeno's paradox
Uhm, regardless, when each next step becomes half the step size of the previous then how on earth can you EVER reach your goal, especially when you go on for infinity dividing your next step by 2? It's impossible.
By the way, there's no such thing as a 'final' step when something really is infinite, even when the difference between infinite and (infinite+1 step more) becomes 'irrelevant' in terms of usage of our language.
Anyways, as fastlane said, you really can only reach your goal this way when your very first step practically gets you there (for example when the whole journey only takes 2 steps in total), since your next step will be half of your last in distance.
Cheers
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