Selvage
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In a woven fabric, the selvage (or selvedge) is the uncut edge of the fabric which is on the right- and left-hand edges as it comes out of the loom. As such it is 'finished' and will not fray because the weft threads double back on themselves.
Very often fabric near the selvage is not usable as it may have a different weave pattern, or may lack pile or prints that are present on the rest of the fabric requiring that the selvage fabric be cut off or hidden in a hem.