For an acnodal cubic the six imaginery inflections disappear, and there remain three real inflections lying in a line.
The oval may unite itself with the infinite branch, or it may dwindle into a point, and we have the crunodal and the acnodal forms respectively; or if simultaneously the oval dwindles into a point and unites itself to the infinite branch, we have the cuspidal form.
crunodal or acnodal), or cuspidal; and we see further that there are two kinds of non-singular curves, the complex and the simplex.
There is thus a complete division into the five kinds, the complex, simplex, crunodal, acnodal and cuspidal.
Each singular kind presents itself as a limit separating two kinds of inferior singularity; the cuspidal separates the crunodal and the acnodal, and these last separate from each other the complex and the simplex.