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I know the process of awarding sportsmanship badge.

The definition

Up voted 100 answers on questions where an answer of yours has a positive score

Does the positive score mean zero, ie equal number of upvotes and downvotes(it may be zero votes)?

Zero is neither positive nor negative.

How SO deals with this?

If I upvote to my competing answer where my answer got zero score, Will it be count towards Sportsmanship Badge?

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If the score on your answer is zero, then it's not positive. In that case, upvoting a competing answer will not count towards the Sportsmanship badge.

No, a positive score does not mean zero. Zero is not positive. Only where your answer has a positive score, will upvotes for competing answers count. Answers of yours that have a non-positive score, which includes those with a zero score, will not mean that competing answers count. Blah blah zalgo he comes blah blah.

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    Zero is not positive. Depends on the definition of positive. For a mathematician working on the real line, it is common for positive to mean >=0 and strictly positive to mean >0. I'm sure that's not the reasoning used on the Stack, but I'm just providing a rationale for the question. – David Heffernan Jun 28 '13 at 8:08

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