so why don't we say, "Don't cross a street without looking both ways",
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But you could - for example if you were ticking off a child for running across the road without looking then you could conceivably say to them 'Don't you ever cross a street again without looking both ways', although I would agree that more normally you would tell them not to cross 'the' road.

(Just having a minor flash back to my youth when they used to run adverts on tv with the Jolly Green Giant (I think) teaching children how to cross the road. It used to finish with the instruction: Never Cross the Road without the Green Cross Code)