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Bracha Rishona and Bracha Acharona are two separate categories that are not connected. For example, rice is mezonos and borei nefashos at the same time. So a mistake in one would not affect the other.


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The Maggid Mishnah in Hilchos Shabbos (17:26) says that one may rely on π=3 It actually is commenting on the Rambam's statement that a circle of circumference three has diameter one. It says that that's "not precise…, but the rabbis were not careful about things that are only required by rabbinical ordinance, and were lenient about it". he says ...


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To start with, both the first and second interpretations of vechai bahem are non-literal explanations. Literal is that you should live your lives by the rules laid out by the mitzvot, or that by following these rules, you will have the reward of life as opposed to the penalty of the opposite. So you are actually asking about a logical extension of the first ...


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