Question:

What is the effect of bittul chometz (annulment of chometz)?
Does it mean that the chometz is no longer in the person’s possession or does it also mean that if one were to mistakenly eat a crumb it would be considered as if one had just eaten dust?

Answer:

According to Tosafos, the effect of bittul chametz is similar to the effect of hefker, and causes the chametz to leave one’s property. The Ran expresses a similar idea, and writes that bittul ensures that the chametz will not be in a person’s domain over Pesach. According to Rashi, the idea of bittul would appear to have more of an effect on the chametz itself, rendering it “as dust.” However, all would agree that it would not be permitted to eat the chametz (even on a Torah level), because by eating it, a person implicitly declares that the chametz is indeed food, and not dust. The fear that he might come to eat it is the reason for which Chazal did not rely on bittul alone, but obligated a person to clear out all of the chametz from his domain: although a person has “annulled” his chametz, eating it would still constitute a Torah prohibition.

Sources:

The principle sugya in which the opinions above are found is Pesachim 6b. Concerning the opinion of Rashi, see especially Maharam Chalava, and Ritva also mentions that after bittul the chametz is no longer considered bread. Concerning the prohibition of eating the chametz after bittul, Maharam Chalava explains that the entire bitul does not apply to eating, and the bread is only considered as dust with regard to the prohibition of bal yera’eh. Others, however, write that the bittul works with regard to everything, but eating the bread would be a cancellation of the bittul, for one reveals that it remains bread.

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