Just a joke proof. Prove or disprove: for any two real numbers a and b such that , then for some integer z.
Suppose that the statement is correct. Let and . Then so that a and b satisfy the hypothesis of the statement. By the statement, there exists an integer z such that . Then by substitution. Subtracting 1.5 from both sides: . But is not an integer. Thus, z is both an integer and not an integer, a contradiction. The hypothesis must be false and the statement is false, which was to be shown.