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I think it might just be a strangely formed sentence where the part "if it contains the item" is not the subject of the report, but a condition:

If it contains the item -> reports that it contains the item (correctly)

If it doesn't contain the item -> may report that it contains the item (incorrectly)

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Nothing wrong with being pedantic when dealing with definitions.

Since we're on the topic of being pedantic, "well, you know, that's just, like... your opinion, man". I'd argue that there's nothing excessive about arguing if A may, in fact, be the opposite of A :)

Certainly not, I'm all for some arguing on the internet.

The logic you wrote is exactly the _opposite_ of what a Bloom filter does.

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