459. A Broken Corner
Tzitzis 1:18
Let’s say that the corner of a garment that has tzitzis attached gets ripped off of the garment. If more than three fingerbreadths were ripped off, it may be reattached, but not if less than three fingerbreadths were ripped off. If the torn-off part of the garment is between the tzitzis and the edge of the garment, it is valid even if only a tiny piece of the fabric still remains. Similarly, if the strings of tzitzis get reduced, they remain valid so long as enough of the string remains to tie a loop. However, if even a single string should get broken off, it is no longer valid.
Tzitzis 2:1
In the Torah, the word techeiles refers to wool dyed a light shade of blue, the color of the sky opposite the sun on a clear day. When referring to tzitzis, it means a specific dye that retains its appearance without changing. Strings dyed blue using any other dye may not be used as tzitzis even if they are the same shade of blue. Wool from a ewe that is the offspring of a goat may not be used for tzitzis.