[Avodah] Chometz: Less than a kezayis

[Akiva Miller via Avodah]

I saw an "advertorial" (that's how the page referred to itself) in the
Mishpacha magazine last year, in issue #607, 12 Nisan 5776, on page 204.
The same page is available on line in a few other magazines, such as page
99 at https://issuu.com/weeklylink.com/docs/vol_10_issue_28

(In the excerpts below, the parentheses and brackets are in the original,
but I did not highlight that which is bold or italics in the original.)

They write in the name of Rav Chaim Pinchos Scheinberg ztz"l:

> The general obligation to check for and get rid of crumbs
> does not apply if the crumbs are less than the size of an
> olive (k'zayis) and are dirty or spoiled enough to deter a
> person from eating them.

And they quote Rabbis Elozor Barclay and Yitzchok Jaeger that:

> If the chometz is dirty then only a piece that is the size
> of a k'zayis (an olive) must be removed.
> If the chometz is edible, then even a smaller [than a kzayis]
> piece that one may be tempted to eat must be removed.

If this is indeed the halacha, then it explains and simplifies several
difficulties I've had over the years. But *is* this the halacha? The page
has very few references to printed sources, and I'd appreciate any mar'eh
m'komos that anyone might offer.

Beyond the lack of references, I have a specific question on this. They
seem to be saying that one may deliberately ignore chometz gamur, and
deliberately *not* get rid of it, provided it is smaller than a kezayis
*and* he is not worried that someone might eat it.

Meiheicha teisa? Have we ever been taught such a thing? We are allowed to
keep a small amount of chometz over Pesach?

I would understand if someone would say that if the chometz is smaller than
a kezayis, then it is a "chetzi shiur", and certain leniencies could be
allowed for difficult situations. But they seem to be going much farther,
saying that chometz less than a kezayis is totally outside the purview of
Bal Yiraeh Ubal Yimatzeh; we would need to get rid of it only if there's a
chance it might be eaten. After all, the shiur for eating is a mashehu.

If all the above is accurate, are there any other examples of something
where a kezayis is assur d'Oraisa, but less than a kezayis is mutar
l'chatchila?

(By the way, I am aware that one can easily take care of his d'Oraisas
simply by being sincere when he does Bitul Chometz. But d'rabanan, we worry
that the bitul was *not* sincere (enough), so I don't know how that would
help.)

Akiva Miller
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