The magnetic poles always exist in pairs.It is not possible to separate the two poles of a magnet.
If a bar magnet is broken at the middle in two parts each part is found to be a magnet.Each part has the property to attract the small iron placed .Each part resist in the North-South direction when suspended such as to swing freely.This shows that the new poles are formed at the broken ends.
If these pieces are broken again and again, each part will still found to be a complete magnet.Each part contains both the poles (N-pole and S-pole).Thus the two poles of a magnet exist simultaneously