Notein taam lifgam — a prohibition that imparts only a spoiled / detrimental taste does not forbid the mixture (derived from the גר: only a נבילה fit for the גר is forbidden); even a slightly spoiled taste suffices, unless the prohibition is the majority and in substance; a dish improved-then-spoiled (or the reverse) remains forbidden; a pot not used for 24 hours (אינה בת יומה) imparts a spoiled taste and does not forbid; the oil and honey of a non-Jew that the meat spoils; and the גוף חריף (spices/pepper) that "improves" (Shulchan Aruch, Yoreh De'ah 103 — 7 se'ifim)
כָּל דָּבָר שֶׁטַּעְמוֹ פָּגוּם — אֵינוֹ אוֹסֵר תַּעֲרֻבְתּוֹ. וַאֲפִלּוּ אֵין טַעְמוֹ פָּגוּם מֵחֲמַת עַצְמוֹ, שֶׁבִּפְנֵי עַצְמוֹ הוּא מֻטְעָם וּמְשֻׁבָּח, אֶלָּא שֶׁפּוֹגֵם תַּעֲרֻבְתּוֹ — מֻתָּר.
Anything whose taste is spoiled does not forbid its mixture. And even if its taste is not spoiled in itself — for on its own it is tasty and excellent — but it spoils the mixture [into which it falls], it is permitted.
Shulchan Aruch, Yoreh De'ah 103:1LEVEL 01
Hebrew text of the 7 se'ifim with a fluent English translation. The principle of notein taam lifgam, the degree of פגם and the distinction טעם / ממשות, the oil and honey of a non-Jew, the pot אינה בת יומה (24h) and the גוף חריף explained with practical cases.
📖 StudyLEVEL 02
In-depth pilpul: the derashah of the גר and the framework טעם / רוב (Taz sk1), the חוכך when one benefits from the quantity more than it spoils the taste (Taz sk4), the נ״ט בר נ״ט דהיתרא of spoon to pot (Taz sk6), the מחלוקת on the honey itself vs. a drink made of honey (Shach sk13-14), and the חתיכה נעשית נבילה of se'if 7 (Shach sk18).
📖 StudyLEVEL 03
Comparative tables (taste alone / substance, majority / מחצה, improved-then-spoiled, בת יומה / אינה בת יומה), golden rules, classic pitfalls (ציר counted as substance, grease בעין, גוף חריף, חנ״נ) and memorization of the 7 se'ifim.
📖 StudyLEVEL 04
The practical halacha according to the Shach, Taz, Pri Megadim and Pitchei Teshuva, then the Sephardic poskim (Yabia Omer, Yalkut Yosef, Or LeTzion) and Ashkenazi poskim. Note: the Shulchan Aruch HaRav does not deal with this siman — this is a level of psak, not "Daat HaRav".
📖 StudyAccording to the Shulchan Aruch (YD 103:1), a prohibition that imparts to the mixture only a spoiled / detrimental taste (notein taam lifgam) does not forbid it, and this even if the prohibition is itself tasty and excellent, as long as it spoils the dish into which it falls. The source (Taz sk1) is derived from the גר: «לֹא תֹאכְלוּ כָל נְבֵלָה לַגֵּר אֲשֶׁר בִּשְׁעָרֶיךָ תִּתְּנֶנָּה» — only a נבילה fit for the גר is called נבילה; what is spoiled to the point of being unfit to eat no longer has the status of a prohibition. For practical halacha, consult your Rav.
No: the פגם need not render the dish inedible — spoiling a little (פוגם קצת) suffices (se'if 2). But there is a distinction: if there is only the taste of the prohibition (טעמו בלבד), without substance, it is permitted even when the prohibition is the majority; whereas when there is substance (ממש) and the prohibition is the majority or even half-and-half (מחצה על מחצה), one does not apply notein taam lifgam until it spoils completely (unfit to eat). It must also spoil from beginning to end (מתחילתו ועד סופו): a dish improved-then-spoiled (משביח ולבסוף פוגם) — or the reverse — remains forbidden. For practical halacha, consult your Rav.
Because the absorbed taste has aged and is deemed spoiled (se'if 5). The pot remains בת יומה as long as 24 hours (מעת לעת) have not passed since the prohibition was cooked in it; afterwards it is אינה בת יומה and the dish cooked in it is permitted (נ״ט לפגם), provided it is rinsed (מודחת), with no grease בעין on its surface — for grease בעין is like a piece of unspoiled prohibition that forbids. The Rama adds that if there is 60 against what is stuck on it, all permit, since the pot is not בת יומה. For practical halacha, consult your Rav.