In various studies concerning computer science or artificial intelligence, in which approximation tools could be applied, there appears a need of gradual approximating descending set sequences X = (X_m) (e.g. of documents, objects, points) formed of elements satisfying some stronger and stronger conditions. Gradual approximations (both: lower and upper ones) are determined by a descending sequence (≌ _j) of equivalence relations, going to be established progressively. Approximations of grade j+1 are better than those of grade j. Approximations determined by ≌_ω, which is the intersection of ≌_j for j < ω, are the most precise.