Standalone expository note by Paul Garrett, verified from the full-name byline on p. 1. Hosted on his University of Minnesota faculty website; the host is not the author.
The document header is dated 19 February 2005; this does not establish a first publication date.
Cited passages: p. 1, theorem for two injections between arbitrary sets and introductory no-choice statement; pp. 1–2, chain types and forward or reversed pairings. The article independently proves its alternative complement pairing.

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