To write a diary - is to note down details on a day to day basis or a regular basis as though you are recording events that have happened during that particular day. To write in a diary - is the act of writing in a diary for that particular moment. You could be writing just anything.
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TakaMy English-Japanese dictianary says:When you write a diary...
is wrong, and it has to be:
When you write in a diary...
But in reality, is it true? Google shows many examples of 'write a diary'...so many that I'm not sure it's wrong...
A Dictionary of the Avant-Gardes
by Richard Kostelanetz - Art - 2001 - 736 pages... to write a d