What property of a magnet determines which side of it is N or S?

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The property that determines which side of a magnet is North or South is its internal alignment of tiny magnetic domains. When a magnet is cut, it does not create a single-pole magnet because each half retains both a North and South pole due to the alignment of these domains. The inability to isolate a magnetic monopole means that every magnet will always have two poles. The discussion humorously suggests that discovering a monopole would lead to significant power, but also hints at commercial interests. Understanding these properties is crucial for grasping the fundamentals of magnetism.
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What property of the magnet determines which side of it is North and which side is South?

I know that we are unable to separate the poles of a magnet (ie cut a magnet in halves and we get two magnets). How come?
 
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A magnet bar consists of numerous tiny magnets (perhalf molecular scale), so you can not separate it into 2 one-pole magnets.
The poles of a magnet allign with the poles of all the tiny magnets.
 
Let's just say that if you ever manage to isolate a magnetic monopole, you will own the planet... until Disney buys you out.
 

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