What if he'd hoped for 18000 spears? The total number of spears hoped for isnt stated, therefore we cannot assume that 6001 is exactly half of the total.
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In this instance we can tell it's 6001 though.
therefore we cannot assume that 6001 is exactly half of the total.
Correct, all we can deduce is the bounds:
Let x be the number of spears hoped for.
6000 < x/2 < 6002
12000 < x < 12004
Edit: fixed error
Less than half and more than half imply strict inequality, so 6000 < x/2 < 6002, so 12001 <= x <= 12003
You're absolutely correct, it should be "<". Since he wished for such an odd number, I wouldn't constrain x to integers though. Maybe he wished for "more than twelve thousand spears"?
Anywhere between 6000.5 and 6001.5 could be exactly half the number of spears he was hoping for assuming he's hoping for whole spears.
Imagine being the guy with half a spear
I sure hope he has the pointy half
He had hoped for precisely 12002 spears.
Or 12003
Or 12001