When does using swapcase twice not return an identical answer?

Question

The Python docs for str.swapcase() say:

Note that it is not necessarily true that s.swapcase().swapcase() == s.

I'm guessing that this has something to do with Unicode; however, I wasn't able to produce a string that changed after exactly two applications of swapcase(). What kind of a string would fail to produce an identical result?

Here's what I tested (acquired here):

>>> testString = '''Bãｃｏл íｐѕüϻ Ꮷ߀ɭｏｒ ｓìｔ äｍéｔ ｑûìｓ àɭïɋüíｐ ｃüｌρä, ϻａｇｎâ èх ѕêԁ ѕｔｒíρ ｓｔêãｋ ｉл ԁò ｕｔ ｓåｌáｍí éхèｒｃìｔáｔïｏл ｐòｒƙ ɭ߀ｉｎ. Téԉԁëｒɭ߀íｎ ｔùｒｋèϒ ѕáûｓáɢè лùɭɭå ｐɑｒïáｔûｒ, ƃáｌｌ ｔíｐ âԁｉρïѕｉｃïԉǥ ɑᏧ ｃ߀ԉｓêｑｕäｔ ϻâｇлã ｖéлïｓｏл. Míлíｍ àｕｔë ѵ߀ɭüρｔåｔｅ ｍòɭɭíｔ ｔｒｉ-ｔíρ ｄèｓêｒùԉｔ. Oｃｃãèｃáｔ ｖëԉｉｓ߀ԉ êХ ｅｉùѕｍ߀ｄ ｓéᏧ ｌáｂｏｒüϻ ｐòｒƙ ｌòïл àｌｉɋûå ìлｃíԁìԁúԉｔ. Sｅｄ ｃòｍϻ߀Ꮷ߀ յｏɰｌ ｏｆｆíｃíä ｐòｒƙ ƅèɭｌｙ ｔéｍρòｒ ｌâƅòｒùϻ ｔâｉɭ ｓρåｒê ｒíｂｓ ｔｏлǥｕｅ ϻêáｔɭòáｆ ｍåɢｎä.  Kｉèɭｂàѕã ｉｎ ｃòлѕêｃｔêｔｕｒ ѵëлíàϻ ｐâｒíɑｔùｒ ｐ߀ｒｋ ɭ߀ｉｎ êｘêｒｃìｔâｔｉòл äｌìɋúíρ ｃâρｉｃｏｌɑ ρｏｒｋ ｔòлɢüê ｄüｉｓ ԁ߀ɭｏｒé ｒêｐｒéｈéԉᏧéｒïｔ. Tèｎԁèｒｌｏｉԉ ëх ｒèρｒéհｅԉԁéｒïｔ ｆûｇíãｔ äｄｉｐìｓｉｃｉԉｇ ｇｒ߀üｎᏧ ｒｏúлｄ, ƅａɭɭ ｔíｐ հàϻƃûｒǥèｒ ѕɦòùｌｄｅｒ ɭåｂ߀ｒûϻ ｔêｍρｏｒ ｒíƃêｙë. Eѕｓè ｈàϻ ѵëԉｉａｍ, åɭíɋùɑ ìｒüｒｅ ρòｒƙ ｃɦｏｐ ԁò ԁ߀ɭｏｒé ｆｒâｎｋｆüｒｔｅｒ ｎüｌｌａ ｐåｓｔｒäϻí ｓàｕｓàｇè ｓèᏧ. Eӽｃêｐｔêüｒ ѕëｄ ｔ-ｂ߀лë հɑϻ, ｅｓѕë ｕｔ ɭàƅｏｒíѕ ƃáｌｌ ｔíρ ｎｏｓｔｒúԁ ｓհ߀üｌｄêｒ ïｎ ｓｈòｒｔ ｒíƅｓ ρáｓｔｒáｍï. Eｓｓé ｈａｍƅûｒǥëｒ ɭäƅòｒé, ｆａｔƃàｃƙ ｔｅԉｄｅｒｌòïｎ ｓհ߀ｒｔ ｒïｂｓ ρｒòìｄéｎｔ ｒｉƅêｙｅ ɭａｂ߀ｒｕｍ. Nｕｌｌɑ ｔüｒԁùｃƙèｎ л߀ｎ, ｓρａｒè ｒìƅｓ ｅӽｃｅρｔｅｕｒ áｄïρìѕìｃïԉǥ êｔ ѕɦｏｒｔ ɭòｉｎ ｄｏｌｏｒë äｎïｍ ｄêѕêｒùлｔ. Sհäлƙｌè ｃúｐïԁäｔáｔ ｐｏｒｋ ｌòïｎ ｍéåｔｂäｌｌ, ԉ߀ｓｔｒｕｄ ｒéｐｒèհéԉԁêｒìｔ ɦɑϻｂｕｒǥêｒ ѕâɭɑϻí Ꮷｏｌ߀ｒè ɑｄ ｌêｂｅｒƙãｓ.  Bｏûｄｉл ｔｏлǥｕê ｃ߀ԉｓèｑûåｔ ｅà ｒüｍρ ƅáｌɭ ｔíρ ѕρâｒé ｒìｂѕ íｎ ｐｒòｉᏧｅｎｔ ｄûｉѕ ϻíлïｍ èíｕѕｍòᏧ ｃ߀ｒԉêᏧ ƃèèｆ ƅɑｃ߀л ｄ߀ｌｏｒè. Cｏｒｎèｄ ƅëèｆ ｄｒûｍｓｔｉｃƙ ｃùｌｐａ, éлïｍ ｂａɭɭ ｔìｐ ϻéａｔｂâｌɭ ｌａｂ߀ｒê ｔｒｉ-ｔïｐ ｖëｎｉｓｏԉ ǥｒｏùԉԁ ｒòùлԁ հɑｍ ｉл èä ｂãｃòｎ. Eѕѕé ìᏧ ѕúԉｔ, ｓհｏùｌｄéｒ ƙïｅɭƃäѕà ãԁｉρｉｓïｃïԉɢ ɦａϻｂûｒｇêｒ úｔ ԁòɭ߀ｒｅ ｆåｔｂäｃƙ ԁ߀ɭòｒ äлïｍ ｔｒï-ｔíｐ. EíùｓϻòᏧ ｎüｌɭã ｌäｂòｒｕϻ лíѕｉ êｘｃéｐｔèúｒ. Oｃｃåéｃåｔ Ꮷüíѕ ԁèｓｅｒüлｔ ｔｏԉǥｕｅ ϳ߀ｗɭ. Rèρｒéɦëԉԁêｒｉｔ áɭïｑúíｐ ｆûǥｉàｔ ｔùｒｋｅｙ ｖéｎｉãϻ ｑüìѕ.''' >>> testString.swapcase().swapcase() == testString True 

Answer 1

This is the case when multiple letters are lower cases of the same letter.

For example, the micro character µ (U+00B5) and the mu character μ (U+03BC):

>>> u'\xb5'.swapcase() u'\u039c' >>> u'\u03bc'.swapcase() u'\u039c' 

The two are different characters, but their uppercase counterparts are the same. This means that when str.swapcase() is applied, they return the same character. However, doing this again can't (and won't) return both letters.

>>> u'\xb5'.swapcase().swapcase() u'\u03bc'