As you can see by the drawing above we could theoretically continue on with this process infinitely, yet never achieving a monopole. A good definition of a magnetic monopole can be found on http://farside.ph.utexas.edu/~rfitzp/teaching/302l/lectures/node62.html. There it says "[magnetic monopoles are] basically the magnetic equivalent of an electric charge. A positive magnetic monopole is an isolated magnetic north pole." This is a good picture to keep in mind because you can have an isolated electric charge that is either positive or negative. This is not the case with magnets. The picture below should provide some insight on how magnetic fields would look around monopoles. (Image Courtesy of http://farside.ph.utexas.edu/~rfitzp/teaching/302l/lectures/node62.html).

As we can see the monopole magnets would act like an isolated charge. The fields radiate radially outward from the north pole (positive charge) and go radially in to the south pole (negative charge). Although magnetic monopoles are believed to exist, they have never been observed experimentally. This results in Maxwell's equation.(Click the link to the left for an extensive look at the Maxwell equations). It is predicted, according to grand unified theories(GUT), that "The charge on magnetic monopoles predicted by GUT's is either 1 or 2gD(Jeon and Longo 1995). " and "The upper limit on the monopole mass is 1026 eV, or 0.2g." (http://scienceworld.wolfram.com/physics/MagneticMonopole.html).

Much time and many resources are given to people trying to find magnetic monopoles as Serway-Beichner says "attempt's to detect [magnetic monopoles] currently make up an active experimental field of investigation". It is important to find these monopoles because it would change the theory around some of the methods solving magnet related problems. For example the Maxwell equations would be shown to be flawed and possibly obsolete.