Certainly! An example of a clone on a set would be the set of all functions that can be constructed from a fixed set of basic functions using a fixed set of operations.

For example, let S be the set {f(x) = x, g(x) = x^2}, and let F be the set of all functions that can be constructed from the basic functions in S using the operations of addition, subtraction, multiplication, and composition. Then F is a clone on the set of real numbers.

To be more precise, F contains all functions of the form p(x) + q(x), p(x) - q(x), p(x)q(x), and p(q(x)), where p(x) and q(x) are any functions that can be constructed from the basic functions in S using the operations of addition, subtraction, and multiplication.

For example, the function h(x) = 2x^2 - 3x + 1 is in F, since it can be constructed from the basic functions in S (namely, g(x) and f(x)) using the operations of addition, subtraction, and multiplication.

Note that F is closed under these operations, meaning that if p(x) and q(x) are in F, then so are p(x) + q(x), p(x) - q(x), p(x)q(x), and p(q(x)). This is what makes F a clone on the set of real numbers.
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