Richard (1905) presented a solution to the paradox from the viewpoint of predicativisim. Richard claimed that the flaw of the paradoxical construction was that the expression for the construction of the real number "r" does not actually define a real number unambiguously, because the statement refers to the construction of an infinite set of real numbers, of which "r" itself is a part. Thus, Richard says, the real number "r" will not be included as any "r""n", because the definition of "r" does not meet the criteria for being included in the sequence of definitions used to construct the sequence "r""n". Contemporary mathematicians agree that the definition of "r" is invalid, but for a different reason. They believe the definition of "r" is invalid because there is no well-defined notion of when an English phrase defines a real number, and so there is no unambiguous way to construct the sequence "r""n".