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That maths equates meeting someone who is dangerous with putting yourself in danger.

You probably walk past rapists, pedophiles and murderers all the time without putting yourself at any serious risk.

Yeah but those people are functional members of society and act relatively rational when compared to untreated severely mentally ill homeless people. Even if you happen to walk by a rapist/murderer/pedo, they're not likely to do anything in broad daylight on a public sidewalk to random passerbys with tons of other people around. The same cannot be said for some homeless.

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