The name lemniscate is sometimes given to any crunodal quartic curve having only one real finite branch which is symmetric about the axis.
For a crunodal cubic the six inflections which disappear are two of them real, the other four imaginary, and there remain two imaginary inflections and one real inflection.
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.
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.