Example 3.15 Given a list of symbols a1, a2, …, am, a string of these symbols is: B1. the empty string, denoted by λ, or B2. any symbol ai, or   R. xy, the concatenation of x and y, where x and y are strings. Since λ represents the empty string, we do not write λ after it has been concatenated with another string. For example, cubsλ = cubs. It shouldn’t be hard to convince yourself that this definition describes any possible “word” in the given symbols. Refer to Example 3.15. Suppose that the symbols can be compared, so for any i and j with i ≠ j, either ai < aj or aj < ai. Modify the definition so that it defines the set of all strings whose symbols are in increasing order.

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