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Both. The carrot is a positive motivation, and the stick is a negative one.
Control theory
In a game with many players, there can be none, one or many winners and none, one or many losers. A positive sum game is one in which the sum of all the winnings is greater than the sum of all the losses. In theory, then, it should be possible for the winners to compensate the losers but still keep some of the positive sum. But that is in theory!
Yes, although the z-scores associated with p-values of 0.01 and 0.05 have special significance, perhaps mostly for historical reasons, all possible z-scores from negative infinity to positive infinity have meaning in statistical theory and practice.
Prime numbers are positive integers that only have two factors. In theory, there is an infinite amount of them.