DNA from a eukaryotic organism is digested with a restriction endonuclease
and the resulting fragments cloned into a plasmid vector. Bacteria transformed by these plasmids collectively contain all of the genes of the organism. This culture of bacteria is refered to as a:
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Gene library
When the genomic DNA is digested by a restriction endonuclease, and all fragments cloned at random into a plasmid vector, then the majority of genetic information will be included in the mixture of bacteria.
Cultures of the bacteria, with each containing only a fraction of the genome, collectively contain all the genes and are called a library.