Talk:Cantor's first set theory article/Archive 1: Difference between revisions

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This is just another flavour of Dedekind's definition of real number. Defining a real number does not make it 'countable', whatever countable means for indeed it is not defined in any way. What is being defined first here - countability or a real number? The Diagonal Argument is very different to this inconsequential theorem. Both the theorem and diagonal argument are flawed. [[Special:Contributions/91.105.179.213|91.105.179.213]] ([[User talk:91.105.179.213|talk]]) 10:21, 19 January 2010 (UTC)
 
: You're confused. The set G you refer to DOES NOT generally contain a member between A and B; in particular, if G is countable then it can be partitioned into such sets A and B such that G contains no such element. And you haven't defined "indeterminate". Countability is used in order to reach the conclusion. If you missed that, you haven't read carefully. [[User:Michael Hardy|Michael Hardy]] ([[User talk:Michael Hardy|talk]]) 14:29, 19 January 2010 (UTC)