Covering Definition/Meaning:

1. Covering of a set S. A finite set of subsets of S whose union is just S itself. The subsets, A₁, A₂..... A_m are said to cover S. If the elements A₁ for i = 1, 2.....m are mutually disjoint, then the covering

(A₁..... A_m)

is called a partition of S.

2. A relationship between two elements of a partially ordered set S. If x and y are elements of S then y covers x if and only if x<y, and whenever x≤z≤y for some element z in S, then either x = z or z = y.

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