
A person can be commanded to do something (“Eat matzah on Pesach!”) or not to do something (“Don’t eat shellfish!”). A mitzvah is either positive or negative, but a single statement can’t be both. A negation, however, is not a separate mitzvah. (We should mention that Rambam uses the Hebrew word sh’lilah.)
What’s a negation? It’s simply the reversal of what a statement would otherwise say. “I did not sleep last night” is the negation of “I slept last night.” It’s not a command at all. In Hebrew, a negation would commonly (but not exclusively) occur when the word “lo” (“no” or “not”) is added. “Lo achalti” (“I did not eat) is the negation of “achalti” (“I ate.”)
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