Prove that the ordered set of all finite or infinite sequenced of binary strings is a tree.
Let S be the set of all finite binary strings, including the empty string. Define a partial order on S by a is ordered under b if and only if b is a prefix of a or there exists strings x, y, and z such that b = x0y and a = x1z. Show that this partial order is in fact a partial order and that (S, <=) is a chain lattice with a top element but no bottom element.
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