Even a Tiny Bit is Not Allowed

Regarding punishments or the obligation to bring a sin-offering, there are certain amounts of eating or doing something forbidden that would require a punishment or an offering. If someone ate less than a certain amount of a forbidden food, for example, he would not be punished. But even less than that amount is still forbidden! One may not eat or do something forbidden, even just a tiny bit.

(See meeting of the Lubavitcher Rebbe King Moshiach Shlita and Rav Mordechai Eliyahu, 6 MarCheshvan 5752 (1991))