# A calculus of the absurd

Suppose that we have a set $$R$$ such that
$$R = \{ A : A \notin A \}$$
That is, “$$R$$ is the set of objects which are not elements of themselves”.
However, is $$R \in R$$? Well, if $$R$$ is in $$R$$, then $$R$$ (by definition of $$R$$) is not in $$R$$. If $$R$$ is not in $$R$$, then $$R$$ (by definition of $$R$$) is in $$R$$. This is a paradox - it cannot be true.