Editing Cantor's diagonal argument (section)

===Diagonalization in broader context===
[[Russell's paradox]] has shown that set theory that includes an [[unrestricted comprehension]] scheme is contradictory.  Note that there is a similarity between the construction of ''T'' and the set in Russell's paradox. Therefore, depending on how we modify the axiom scheme of comprehension in order to avoid Russell's paradox, arguments such as the non-existence of a set of all sets may or may not remain valid.

Analogues of the diagonal argument are widely used in mathematics to prove the existence or nonexistence of certain objects. For example, the conventional proof of the unsolvability of the [[halting problem]] is essentially a diagonal argument.  Also, diagonalization was originally used to show the existence of arbitrarily hard [[complexity classes]] and played a key role in early attempts to prove [[P versus NP|P does not equal NP]].