The interesting number paradox is an informal paradox in which an attempted classification of positive integers as interesting or uninteresting leads to the claim that all are interesting. Suppose that the uninteresting positive integers form a nonempty set. By the well ordering principle, it has a smallest member. Being the smallest uninteresting number is then declared interesting, contradicting its membership in the uninteresting set (Gardner 1958, p. 96).
The argument supplies no fixed mathematical definition of "interesting." If a specified subset 
of the positive integers
omits any member, the smallest positive
integer outside 
remains outside 
. Finding its description interesting does not establish that
it satisfies the predicate defining membership in 
.
