We study numerically the memory that forgets, introduced in 1986 by Parisi by bounding the synaptic strength, with a mechanism that avoids confusion; allows remembering the pattern learned more recently; and has a physiologically very well-defined meaning. We analyze a number of features of this learning for a finite number of neurons and finite number of patterns. We discuss how the system behaves in the large but finite $N$ limit. We analyze the basin of attraction of the patterns that have been learned, and we show that it is exponentially small in the age of the pattern.