Something wrong with str.upper().lower() chain?

[magniff]

BPO	27608
Nosy	@rhettinger, @vstinner, @ezio-melotti, @magniff

^{Note: these values reflect the state of the issue at the time it was migrated and might not reflect the current state.}

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GitHub fields:

assignee = None
closed_at = <Date 2016-07-24.21:20:29.942>
created_at = <Date 2016-07-24.17:37:20.640>
labels = ['type-bug', 'invalid', 'expert-unicode']
title = 'Something wrong with str.upper().lower() chain?'
updated_at = <Date 2016-07-25.02:25:20.020>
user = 'https://github.com/magniff'

bugs.python.org fields:

activity = <Date 2016-07-25.02:25:20.020>
actor = 'abarry'
assignee = 'none'
closed = True
closed_date = <Date 2016-07-24.21:20:29.942>
closer = 'magniff'
components = ['Unicode']
creation = <Date 2016-07-24.17:37:20.640>
creator = 'magniff'
dependencies = []
files = []
hgrepos = []
issue_num = 27608
keywords = []
message_count = 5.0
messages = ['271174', '271175', '271176', '271177', '271182']
nosy_count = 4.0
nosy_names = ['rhettinger', 'vstinner', 'ezio.melotti', 'magniff']
pr_nums = []
priority = 'normal'
resolution = 'not a bug'
stage = 'resolved'
status = 'closed'
superseder = None
type = 'behavior'
url = 'https://bugs.python.org/issue27608'
versions = ['Python 3.4', 'Python 3.5', 'Python 3.6']

[magniff]

For some reason 
>>> 'µ'.upper().lower() == 'µ'
False

[magniff]

Note, that
>>> ord('µ')
181

there is another Mu like symbol chr(956), on which this code passes

[magniff]

So, yes, unicode table seems to be a bit inconsistent. In str documentation it worth to emphasize that something.upper().lower() in general not equals to something.

[rhettinger]

Here is a little more detail on what is occurring:

>>> from unicodedata import *
>>> c = 'µ'
>>> for s in (c, c.lower(), c.upper(), c.lower().upper(), c.upper().lower()):
	print(s, ord(s), name(s), category(s))
	
µ 181 MICRO SIGN Ll
µ 181 MICRO SIGN Ll
Μ 924 GREEK CAPITAL LETTER MU Lu
Μ 924 GREEK CAPITAL LETTER MU Lu
μ 956 GREEK SMALL LETTER MU Ll

[magniff]

Conclusion made: not a bug (not a python bug at least).