Is writing "wishing you the best of health" at end of a letter considered a sentence fragment?
closed as unclear what you're asking by Nathaniel, Drew, ab2, Hellion, Mari-Lou A Jan 26 '16 at 9:45
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That part of the letter is called the 'closing'. A more formal term is 'valediction'. It is perfectly fine as a fragment, or even a single word (i.e., 'Sincerely,').
The beginning/greeting of the letter is called the 'opening' or 'salutation'. This is also fine as a single word or fragment.
This picture shows the sections of the standard letter format:
Formerly the close to a formal letter would be something like
Wishing you the best of health, I remain,
(with a handwritten signature above the name), which is both complimentary and grammatical.
It is no longer considered necessary to go to such lengths, but some pieces, such as 'Yours' or 'wishing you all the best' are often inserted in an attempt to dignify the message. They are certainly fragments if not fossils of a bygone age, but will be understood to be purely formalities. Whether they are helpful in any particular case is of course a stylistic judgement.