The world of flowering plants -- the angiosperms -- don't divide neatly into monocots and dicots. Studies using gene sequencing have shown that the situation actually looks more like the branch from the Tree of Life shown below (Many experts would disagree in some or most details):

monocots & dicots
Diagram redrawn from an online paper by Soltis, Soltis & Edwards found at the Tree of Life project. On that page, dated 2005, there is a much more detailed discussion of the new concepts, with pictures and an extensive list of references. As of 2015, about 352,000 species of flowering plants, or angiosperms, were recognized, classified in 405 families. More info at ThePlantList.Org site.

Traditionally all the above groupings other than monocots were regarded as dicots. Today the monocots are kept as before, but the dicots have been split into the various groupings shown. The eudicots, or "pure dicots," are what remains of the former dicot group. An enormous number of species are still regarded as eudicots -- about 75% of all flowering plants!

Relative to the vast number of species among the monocots and eudicots, a fairly small number of species belong to the other groupings. The most numerous non-monocot and non-eudicot species are found in the large-flowered magnoliides and the waterlilies of the Nymphaeaceae. Therefore, we amateurs are not being grossly messy by continuing to think in the simple, "outdated" terms of monocots and dicots.