Checking Books for Chametz

Question: Do one’s books need to be checked for chametz or sold before Pesach?

Answer: The gemara (Pesachim 6b), in discussing the need for bitul (nullification of) chametz, says that peirurim (small pieces or crumbs) do not need bitul, as there is no bal yeira’eh (prohibition to possess) because they are insignificant. Important poskim (including Ritva, Pesachim 7a; Pri Chadash, Orach Chayim 444:4; each refers to those who are stringent) understand from here that there is no need to discard crumbs.
On the other hand, the gemara (Pesachim 45b) says that pieces of dough under the size of a k’zayit that are stuck to a utensil (even one not used on Pesach) need to be discarded. The Shulchan Aruch (OC 460:3) requires bitul on pieces of dough that fall while making matza. Several distinctions may impact on the need to remove small pieces and help answer contradictions: dough (requires disposal) vs. bread crumbs (do not) (Magen Avraham 260:2); whether the pieces are clean (Mishna Berura 442:33); whether they are in a prominent place (see Shut Nitei Gavriel, Pesach 1).
You ask not about disposing known peirurim but searching for them, and we note the following halachot. One must check only the type of room that one would enter holding a piece of chametz (see Pesachim 8a with Rashi); we are not concerned about crumbs falling. If a toddler took chametz to a place where bedikat chametz was done and we found peirurim, we can assume the rest was eaten and do not need to re-check (Shulchan Aruch, OC 439:1), despite the likelihood of additional crumbs.
Perhaps the first major posek to require (not just out of piety) checking for crumbs is the Chayei Adam (II:119:6). He learns from the idea of checking in crevices (Pesachim 7a) that bedika is needed for crumbs, reasoning that despite the lack of bal yeira’eh, there is concern one may come to eat them. The Chazon Ish (OC 116:18) goes further, saying that if he does not check for crumbs, they are forbidden after Pesach, and he is perhaps the first to say that one must check his sefarim. This is not obvious from the Chayei Adam, as one does not purposely put food on sefarim and it is also unlikely that one would come to eat crumbs stuck to a book or trapped in its binding. The Mishna Berura (442:33), for example, says that everyone agrees that a piece of less than a k’zayit of soiled chametz does not need to be discarded.
The S’fat Emet (Pesachim 6b) proposes other reasons not to check for crumbs: 1) It is too much work for Chazal to have made it necessary; 2) It is anyway impossible to succeed in removing all crumbs. These points lead us to the following observation. What many people call "cleaning" their books in a few hours would not suffice if the obligation was rigorous; it would take tens if not hundreds of hours. While that might be a modern problem (a modern library of bound books is harder to check than a few scrolls), it is still illogical from the perspective of "halachic history" that discussion of the problem of checking books surfaces only in the 20th century.
The practice of some to "shake out" books is reasonable as a stringency (or spring cleaning), but realize that checking books for chametz is no more than that. The idea that some illustrious contemporary rabbanim suggest of selling sefarim to a non-Jew is less wasteful of precious time than properly checking them. However, this is a recent invention not imagined by those who instituted mechirat chametz for sell valuable chametz . How can one be required to sell a valuable collection of sefarim (and raise questions about the sale’s seriousness) and take them out of use for Pesach to avoid a problem very few poskim believe exists (see Chazon Ovadia, Pesach p. 38)? My personal choice of halacha/chumra is to clean bookshelves, not to use the same books at the table for during the year and for Pesach, and to sell bentchers. Important sources (see Shulchan Aruch OC 442:6) say not to belittle extra-halachic stringency regarding chametz. However, we oppose making new chumrot with a weak basis standard.