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However, it demonstrates a general technique that has since been used in a wide range of proofs,<ref>{{cite book |title=The Logic of Infinity |edition=illustrated |first1=Barnaby |last1=Sheppard |publisher=Cambridge University Press |year=2014 |isbn=978-1-107-05831-6 |page=73 |url=https://books.google.com/books?id=RXzsAwAAQBAJ}} [https://books.google.com/books?id=RXzsAwAAQBAJ&pg=PA73 Extract of page 73]</ref> including the first of [[Gödel's incompleteness theorems]]<ref name="Simmons1993"/> and Turing's answer to the ''[[Entscheidungsproblem]]''. Diagonalization arguments are often also the source of contradictions like [[Russell's paradox]]<ref>{{cite book|url=http://plato.stanford.edu/entries/russell-paradox|title=Russell's paradox|year=2021|publisher=Stanford encyclopedia of philosophy|archive-date=30 August 2022|access-date=12 July 2016|archive-url=https://web.archive.org/web/20220830154759/https://plato.stanford.edu/entries/russell-paradox/|url-status=live}}</ref><ref>{{cite book|author=Bertrand Russell|title=Principles of mathematics|pages=363–366|publisher=Norton|year=1931}}</ref> and [[Richard's paradox]].<ref name="Simmons1993"/>{{rp|27}}
== [[Uncountable set]] ==
Cantor considered the set ''T'' of all infinite [[sequences]] of [[binary digits]] (i.e. each digit is zero or one).<ref group=note>Cantor used "''m'' and "''w''" instead of "0" and "1", "''M''" instead of "''T''", and "''E''<sub>''i''</sub>" instead of "''s''<sub>''i''</sub>".</ref>
He begins with a [[constructive proof]] of the following [[Lemma (mathematics)|lemma]]:
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