C
Colonel Harlan Sanders
"Clearly wrong" means "the statement or text x that declares 'the
statement or text y is wrong' is true and it is clear". It does not
EVER mean that "the statement or text y is clear and wrong".
Your authority for this rule? The Word of Nilges?
In mathematics, clarity has only one meaning, and that is validity.
You can provide a citation for this interesting definition?
A work of French poetry, perhaps? A conversation you had with John
Nash?
A proof in mathematics cannot be clear and wrong. This is because at
the point of failure, it is unclear.
Rubbish.
When correcting a student's maths, if they have arrived a wrong
result, and have done so in a "clear" manner, it is easy to discover
and point out the error. Clarity helps one to arrive at truth, it also
make it easier to detect untruth, but it does not preclude untruth.
Anyway, you're just arguing from your own definition, again, The Word
of Nilges.
Whatever the meaning of clear in a mathematical context, it has no
relevance to the use when discussing a work of prose. Hint: that's
why the OED has over 30 meanings for the word. Different context,
different meaning.
But you (now) don't believe in dictionaries, right?