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suppose a new user question got so many downvotes, will his reputation go to a negative value.

ie, a new user might with 10 reputation,

and got six downvotes for his question (assume that a downvote costs 2 reputation).

what will be his reputation.

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up vote 7 down vote accepted

No, 1 is the lowest possible reputation.

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...which doesn't mean it's fine to ask such a terrible question. – badp Jan 21 '11 at 8:45
No, when evil Jeff took over for a day (the one without the goatee), reputation mysteriously turned into a signed integer. They just use abs() when displaying it so certain people don't feel bad .. – Tim Post Jan 21 '11 at 8:59

Also to add if I were to have a downvote when I have 1 it will not be taken away when I get say an upvote.

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