So shocking, surprising, or amazing that it's hard to believe; can also mean extremely good.
From 'un-' (not) plus 'believe' (from Old English 'gelyfan'), the prefix 'un-' was added in the 1600s to create the meaning 'not able to be believed.'
In casual speech, 'unbelievable' has flipped meaning—people now use it to praise something awesome rather than express doubt, showing how intensifiers in English constantly get recycled and repurposed.
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