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A cardinal tree (or trie) of degree k, by analogy with cardinal numbers and by opposition with ordinal trees, is: a rooted tree in which each node has k positions for an edge——to a child. Each node has up to k children and each child of a given node is labeled by a unique integer from the——set {1, "2," . . . , k}. For instance, a binary tree is a cardinal tree of degree 2.