Julio:

>  Sabri's mathematician gave up because he interpreted continuity the wrong 
> way.

Actually, I formulated the problem in the wrong way: the mathematician
could have been right. I did not tell you the distance between the
princess and the competitors, and the length of the initial step of
each man could have taken. Depending on these, it may be possible for
one man or both to reach the princess in a finite number of steps or
the other way around.

But when it comes to what Michael L said, we neither know the distance
between us and the target, nor the length of the initial step when can
take, even if the each of the next steps will be half of the previous
one. So, math does not work here, because we do not know what exactly
the problem is. Maybe poetry would help and this is one of my favorite
poems from Turkey, and the poet is not even a poet, he was a writer of
satire:

My father Abdulaziz Efendi
Searched for a treasure throughout his life
As if himself buried it
No one else knew where it was buried
Before finding what he searched for
Exhausted in his eighty-three

I come from a diggers' family
Some of us dig for gold, some of us for love
Yet, all of us in our hearts have this fantasy
I know I can never find it
But still search for the nonexistent
And die before finding it, just like my daddy

Our kind is going extinct as the time goes by my son
Continue this inheritance from our past
Don't let this arthritis dry for the humankind
Even if you know there does not one, search for a treasure imagined in your mind
For to live is to search for the treasure buried in your heart

Aziz Nesin, 1983
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