Shabbos Chapter 13, Mishnah 1. This chapter opens with a discussion of the laws of weaving, and in the Mishnah before us we will examine the dispute between Rabbi Eliezer and the Sages regarding the number of threads that creates liability for the labor of weaving.
Rabbi Eliezer's opinion:
"Shelosha chutin bat'chilah" - one who weaves at the very beginning of the weaving process becomes liable only with three threads. This measure differs from the Mishnah we learned in the seventh chapter, in the listing of the labors, where it stated that one who weaves two threads is liable.
"V'achas al ha'arig" - if there is already a piece of cloth that has been partially woven, and the person is merely adding to it, a single thread is enough to create liability.
So according to Rabbi Eliezer: at the start of the weaving - three threads; when adding to existing woven cloth - one thread.
The opinion of the Sages:
The Sages represent the view presented in the Mishnah in the seventh chapter: "Bein bat'chilah bein basof" - one consistent measure for every manner of weaving, two threads. The beginning does not require three as Rabbi Eliezer holds, nor does adding suffice with one thread as he says, but rather two threads in every case.
What is the "end" being discussed?
It is important to note that when the Mishnah says "whether at the beginning or at the end," it does not mean the end in its literal sense, the actual completion of weaving the garment. For when the weaving of the garment is finished, the final thread does not necessarily create liability for the labor of weaving, but rather for makeh b'patish - the final hammer blow, the completion of a task, which is a labor in its own right.
Rather, the intent is a situation where woven cloth already exists, and it is directed at Rabbi Eliezer's words: when this is not the initial weaving but an addition to what already exists, one thread is not enough as Rabbi Eliezer holds, but two threads are required - both at the beginning and when adding to an existing garment. At the actual completion, however, the weaving would be accomplished with only a single thread.
In summary: in this Mishnah, Rabbi Eliezer and the Sages dispute the measure for the labor of weaving. According to Rabbi Eliezer - three threads at the beginning and one thread onto existing woven cloth; according to the Sages - two threads, both at the beginning and when adding to what already exists, in accordance with the Mishnah in the seventh chapter. And we clarified that "end" does not mean the actual completion of the garment, since there the liability is on account of makeh b'patish, and with only a single thread.