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If you carry out the first experiment conscientiously, you will find that you will not find a magnet that experiences only attraction or only repulsion compared to the north pole of another magnet. That is, each magnet has at least one north pole and one south pole. No magnetic monopoles have yet been found.
One could now come up with the idea of obtaining a single north pole and a single south pole by dividing a bar magnet. You can see, however, that when dividing, all fragments again have a north pole and a south pole.