Editing Countable set (section)

==A note on terminology <span class="anchor" id="Terminology"></span>==
Although the terms "countable" and "countably infinite" as defined here are quite common, the terminology is not universal.<ref>{{cite book |last1=Manetti |first1=Marco |title=Topology |date=19 June 2015 |publisher=Springer |isbn=978-3-319-16958-3 |page=26 |url=https://books.google.com/books?id=89zyCQAAQBAJ&pg=PA26 |language=en}}</ref> An alternative style uses ''countable'' to mean what is here called countably infinite, and ''at most countable'' to mean what is here called countable.<ref name="Rudin">{{Harvard citation no brackets|Rudin|1976|loc=Chapter 2}}</ref><ref>{{harvnb|Tao|2016|p=181}}</ref>

The terms ''enumerable''<ref>{{Harvard citation no brackets|Kamke|1950|page=2}}</ref> and '''denumerable'''<ref name="Lang">{{Harvard citation no brackets|Lang|1993|loc=§2 of Chapter I}}</ref><ref name="Apostol">{{Harvard citation no brackets|Apostol|1969|loc=Chapter 1.14|p=23}}</ref> may also be used, e.g. referring to countable and countably infinite respectively,<ref>{{cite book |last1=Thierry |first1=Vialar |title=Handbook of Mathematics |date=4 April 2017 |publisher=BoD - Books on Demand |isbn=978-2-9551990-1-5 |page=24 |url=https://books.google.com/books?id=RkepDgAAQBAJ&pg=PA24 |language=en}}</ref> definitions vary and care is needed respecting the difference with [[Recursively enumerable language|recursively enumerable]].<ref>{{cite book |last1=Mukherjee |first1=Subir Kumar |title=First Course in Real Analysis |date=2009 |publisher=Academic Publishers |isbn=978-81-89781-90-3 |page=22 |url=https://books.google.com/books?id=n5AhsN5UQ8IC&pg=PA22 |language=en}}</ref>