I play tetris too (hkgwife)

Race #18496

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Official speed 111.60 wpm (39.89 seconds elapsed during race)
Race Start May 9, 2019 9:26:48am UTC
Race Finish May 9, 2019 9:27:28am UTC
Outcome Win (1 of 2)
Accuracy 97.0%
Points 119.04
Text #3640570 (Length: 371 characters)

Property (c) is known as countable additivity. It is not something that can be proved, but it is like an assumption or an axiom. In our experience, we have seen that operating as if the assumption is correct leads to useful and credible answers to many problems, so we accept it as a reasonable assumption. Not all probabilists agree that countable additivity is natural.