Does SUM discard rows that have 0 values?

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No. The SUM function, as well as all other aggregate functions, includes all non-NULL values, and zero is non-NULL. NULLs are ignored, but NULLs are not the same as zeroes.

But when you stop and think about it, what would the difference to the final answer be if zeroes were excluded, as compared to included? Would the answer be any different?