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 in the middle in two parts, each part is found to be a magnet. Each part has the property to attract small iron pieces. Each part rests in the North-South direction when suspended freely. This shows that new poles are formed at the broken ends.
If these pieces are broken again and again, each part will still be a complete magnet. Each part will contain both the poles (N-pole and S-pole).
Thus, the two poles of a magnet exist in pairs.