Talk:Cantor's first set theory article/Archive 2: Difference between revisions

Revision as of 04:56, 7 May 2016

Revision as of 06:12, 7 May 2016

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(1) The standard imposition of order on all the non-negative rational numbers:

{ 0, . . ., 1/4, . . ., 1/2, . . ., 3/4, . . ., 1, . . ., 5/4, . . ., 3/2, . . ., 7/4, . . ., 2, . . ., 9/4, . . . }

is not a well-ordering &mdash#8212; because, for example, there is no positive rational number immediately following 0.

(2) The following imposition of order on all the non-negative rational numbers is a well-ordering but not a countable ordering or enumeration:

{ 0, 1, 2, 3, . . ., 1/2, 3/2, 5/2, . . ., 1/3, 2/3, 4/3, . . ., 1/4, 3/4, 5/4, . . ., 1/5, 2/5, 3/5, . . . }