I have read many defferent versions of the Ross-Littlewood Paradox.
This post: Fun quiz: where did the infinitely many candies come from?
This post: Paradox: increasing sequence that goes to $0$?
This post: A strange puzzle having two possible solutions
And many others.
In all of them, a great effort is made to note that actions are performed in decreasing time intervals (1/2 second, 1/4 second, 1/8 second...). I am wondering why this specification is so important to the paradox? I understand that it stops the infinite steps from taking infinite time. The thing is the steps must then be performed infinitely fast.
Why is it that performing actions infinitely fast is so much more believable than performing actions for an infinite amount of time? In my opinion the latter is more plausible. Also why is believability so important for a paradox which is clearly impossible to execute?
Edit: I also wanted to note that there are similar things where we don't seem to need this kind of action. For example the Infinite Monkey Theorem. Why is it important in one and not the other?
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