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From: Chris Angelico <rosuav@gmail.com>
Newsgroups: comp.lang.python
Subject: Re: Not x.islower() has different output than x.isupper() in list output...
Date: Tue, 3 May 2016 20:25:17 +1000
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On Tue, May 3, 2016 at 8:00 PM,  <pavlovevidence@gmail.com> wrote:
>
> What you should have been expecting is a symmetry.  Say you have a string G.  islower(G) will return a certain result.  Now take every letter in G and swap the case, and call that string g.  isupper(g) will always return the same result is islower(G).
>
> More succinctly, for any string x, the following is always ture:
>
> islower(x) == isupper(swapcase(x))
>
> But that is not the same thing, and does not imply, as the following identity (which it turns out is not always true, as we've seen):
>
> islower(x) == not isupper(x)
>
>
> Another example of functions that behave like this are ispositive and isnegative.  The identity "ispositive(x) == isnegative(-x)" is always true.  However, "ispositive(x) == not isnegative(x)" is false if x == 0.
>

This assumes, of course, that there is a function swapcase which can
return a string with case inverted. I'm not sure such a function
exists.

ChrisA