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Certain issurim (forbidden things) can become batel (halachically nullified) if they were unintentionally mixed in heter (permitted things). In order for this to happen, the heter must outnumber the issur . Depending on what the issur is, the necessary measurement may be 1/60 (taste), 1/100 (terumah) 1/200 (kilayei hakerem and orla) or just a simple rov (majority).

However some things "never" become batel; they are assur even b'mashehu, that is, even in the smallest amount. The classic example of this is chametz (leaven) on Pesach, which is assur even in the minutest proportions.

However, I have been told by a Rov that even mashehu has a shiur (measurement) in which it becomes batel. The example I heard was that the Kinneret's water does not all become assur just because someone dumped chametz there on Pesach. (Yes, I'm aware that some are machmir on this, but let's leave that out, shall we?)

What is this shiur? Is it just a vague "whole lot" kind of feeling? Has any Rov quantified it, or said that it cannot be thus quantified?

Related: tap water on Pesach (Specifically Shalom's answer)

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HodofHod
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    similar http://judaism.stackexchange.com/q/14811/759 – Double AA Apr 21 '13 at 05:33
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    I'm not sure about your specific case, but there is a disagreement among the Poskim if a Mashehu from a mixture that was Assur BeMashehu falls into something else, if that second thing is also Assur. Google " תרי משהוין לא אמרינן". Also, I didn't read the whole thing, but it looks like this Ha'arah may help you out: http://www.haoros.com/Archive/index.asp?kovetz=833&cat=3&haoro=3 – Menachem Aug 07 '13 at 21:14
  • Related: http://judaism.stackexchange.com/a/28589 – msh210 Aug 11 '13 at 18:18
  • isnt this a mefurash gemara in beitzah – sam Mar 09 '17 at 05:44

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R' Blumenkranz in his Pesach Guide discusses homeopathic solutions, and is mattir based on them statistically not containing a single molecule. So according to him, a single molecule constitutes mashehu. E.g. mashehu chametz on pesach of table vinegar is 9.58×10-44 oz, considering only the the acetic acid part.

Adám
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    Does he say that if they contained a molecule they would be assur? Or is he only saying that there isn't a molecule to avoid having to deal with mashehu? – HodofHod Aug 07 '13 at 20:50
  • When we are talking about bitul, we are discussing proportions. For example, bitul b'rov requires majority kosher, while bitul b'shishim requires 60 parts kosher to one part non-kosher. Are you attempting to contradict the premise of this question which says that there is some shiur in which mashehu becomes batel? – Daniel Aug 07 '13 at 21:16
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    Also what do you mean by "statistically not containing a single molecule"? – Daniel Aug 07 '13 at 21:16
  • @HodofHod Good point. I will go and take a closer look. However, the question was on how much a mashehu is. Surely a molecule is mashehu, and less than that cannot be for particle-physical reasons. – Adám Aug 08 '13 at 14:07
  • @Daniel Mashehu is not a proportion, it is a shiur: the minimum amount which is assur. Just like a kezayis pork is assur mid'oraysa. (Let's not get into chezi shiur...) Statistically: E.g. If you have a single molecule chametz floating around in a cup water, and you take out a drop, the chametz will likely remain in the cup, but it just may have been in the drop you took out. – Adám Aug 08 '13 at 14:25
  • @NBZ 2 things. First of all: Suppose you somehow know that there is exactly one chametz molecule in a cup of water, and you pour out 50.01% of the water. Does that mean that there is now statistically no chametz in the water? Second of all: is there even such a thing as a molecule of chametz? There is no such thing, for example, as a molecule of flour. Flour is made up of various chemicals which together make chametz, but separately could go into non-chametz things. So if you take a molecule of that chemical, does it matter if you took it from flour? – Daniel Aug 08 '13 at 14:48
  • @Daniel 1. Not "no chametz", 50.01% chance that there isn't any. A related question could be: "How sure do you have to be in Judaism generally? E.g. that there is no chametz, that you didn't scratch your hair, that you are not a mamzer..." 2. Yes. (Flour actually isn't chametz. See Blumenkrantz for a scientific definition.) A certain chametz is fermented wheat, i.e. alcohol, which is uniformly consisting of (water and) chametz ethanol molecules, CH3CH2OH. Further fermentation gives vinegar, of which a single acetic acid molecule, CH3COOH, is identifiable as chametz. – Adám Aug 08 '13 at 15:30