To choose an arbitrary member of a set is to choose any member of the set without restriction.^{[2]} In math writing, we sometimes want to state that you can pick any member of a set without restriction, and the statement is still true. For real numbers, this means that you can pick any real number, and the statement is true. An example of this is the statement, "Let x be an arbitrary integer." This means that x can be any integer.
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