Impossible or extremely difficult to read because the text is unclear, illegible, or written in a confusing way.
Prefix 'un-' (not) combined with 'readable' (able to be read). 'Read' comes from Old English 'raedan.' The prefix 'un-' became the standard way to create opposite meanings in English.
Doctors' handwriting is famously 'unreadable,' which actually became a serious safety problem in hospitals—so many medication errors happened because pharmacists couldn't read prescriptions that hospitals now require digital systems!
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